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BUDGET    OF    PAEADOXES. 


LONDOM  :     PRINTED     BY 

SPOTTISWOODE    AND    CO.,    STEW-STREET    iQtJAEH 
A.VU    PARLIAMENT     fcTUKKT 


BUDGET    OF    PARADOXES, 


BT 


AUGUSTUS    DE    MORGAN, 

F.R.A.S.  &  C.P.S. 

OF  TRINITY  COLLEGE,  CAMB1UDGB. 


[REPRINTED,    WITH    THE    AUTHOR'S    ADDITIONS,    FROM    THE    ' 


'  Ut  agendo  snrgamus  arguendo  gustamus.' 
PTOCHODOKIAKCHUS 


LONDON : 
LONGMANS,    GREEN,    AND    CO. 

1872. 


A/I    rujhtt    referred. 


AC 


EDITOR'S    PREFACE. 


IT  is  not  without  hesitation  that  I  have  taken  upon  myself 
the  editorship  of  a  work  left  avowedly  imperfect  by  the 
author,  and,  from  its  miscellaneous  and  discursive  character, 
difficult  of  completion  with  due  regard  to  editorial  limita- 
tions by  a  less  able  hand. 

Had  the  author  lived  to  carry  out  his  purpose  he  would 
have  looked  through  his  Budget  again,  amplifying  and 
probably  rearranging  some  of  its  contents.  He  had  collected 
materials  for  further  illustration  of  Paradox  of  the  kind 
treated  of  in  this  book  ;  and  he  meant  to  write  a  second 
part,  in  which  the  contradictions  and  inconsistencies  of 
orthodox  learning  would  have  been  subjected  to  the  same 
scrutiny  and  castigation  as  heterodox  ignorance  had  already 
received. 

It  will  be  seen  that  the  present  volume  contains  more 
than  the  Athenaeum  Budget.  Some  of  the  additions  formed 
a  Supplement  to  the  original  articles.  These  supplementary 
paragraphs  were,  by  the  author,  placed  after  those  to  which 
they  respectively  referred,  being  distinguished  from  the  rest 
of  the  text  by  brackets.  I  have  omitted  these  brackets  as 
useless,  except  where  they  were  needed  to  indicate  sub- 
sequent writing. 


Vl  EDITOR'S    PREFACE. 

Another  and  a  larger  portion  of  the  work  consists  of 
discussion  of  matters  of  contemporary  interest,  for  the 
Budget  was  in  some  degree  a  receptacle  for  the  author's 
thoughts  on  any  literary,  scientific,  or  social  question. 
Having  grown  thus  gradually  to  its  present  size,  the  book 
as  it  was  left  was  not  quite  in  a  fit  condition  for  publication, 
but  the  alterations  which  have  been  made  are  slight  and 
few,  being  in  most  cases  verbal  and  such  as  the  sense 
absolutely  required,  or  transpositions  of  sentences  to  secure 
coherence  with  the  rest,  in  places  where  the  author,  in  his 
more  recent  insertion  of  them,  had  overlooked  the  connexion 
in  which  they  stood.  In  no  case  has  the  meaning  been  in 
any  degree  modified  or  interfered  with. 

One  rather  large  omission  must  be  mentioned  here.  It 
is  an  account  of  the  quarrel  between  Sir  James  South  and 
Mr.  Troughton  on  the  mounting,  &c.  of  the  equatorial 
telescope  at  Campden  Hill.  At  some  future  time  when  the 
affair  has  passed  entirely  out  of  the  memory  of  living 
Astronomers,  the  appreciative  sketch,  which  is  omitted  in 
this  edition  of  the  Budget,  will  be  an  interesting  piece  of 
history  and  study  of  character. 

A  very  small  portion  of  Mr.  James  Smith's  circle-squaring 
has  been  left  out,  with  a  still  smaller  portion  of  Mr.  De 
Morgan's  answers  to  that  Cyclometrical  Paradoxer. 

In  more  than  one  place  repetitions,  which  would  have 
disappeared  under  the  author's  revision,  have  been  allowed 
to  remain,  because  they  could  not  have  been  taken  away 
without  leaving  a  hiatus,  not  easy  to  fill  up  without  damage 
to  the  author's  meaning. 


EDITOR'S    PREFACE.  vii 

I  give  these  explanations  in  obedience  to  the  rules  laid 
down  for  the  guidance  of  editors  at  page  11.  If  any  apology 
for  the  fragmentary  character  of  the  book  be  thought 
necessary,  it  may  be  found  in  the  author's  own  words 
at  page  438. 

The  publication  of  the  Budget  could  not  have  been 
delayed  without  lessening  the  interest  attaching  to  the 
writer's  thoughts  upon  questions  of  our  own  day.  I  trust 
that,  incomplete  as  the  work  is  compared  with  what  it 
might  have  been,  I  shall  not  be  held  mistaken  in  giving  it 
to  the  world.  Bather  let  me  hope  that  it  will  be  welcomed 
as  an  old  friend  returning  under  great  disadvantages,  but 
bringing  a  pleasant  remembrance  of  the  amusement  which 
its  weekly  appearance  in  the  Athenceum  gave  to  both  writer 
and  reader. 

The  Paradoxes  are  dealt  with  in  chronological  order. 
This  will  be  a  guide  to  the  reader,  and  with  the  alphabetical 
Index  of  Names,  &c.,  will,  I  trust,  obviate  all  difficulty  of 
reference. 

SOPHIA  DE  MORGAN. 

6  MERTON  ROID,   PRIMROSE  HILL. 


Erratum. 
Page  40,  line  27,  for  Litchfield  read  Liehfield. 


A   BUDGET 

OP 


PARADOXES 


INTKODUCTOKY. 

IF  I  had  before  me  a  fly  and  an  elephant,  having  rever  seen 
more  than  one  such  magnitude  of  either  kind ;  and  if  the  fly 
were  to  endeavour  to  persuade  me  that  he  was  larger  than  the 
elephan^  I  might  by  possibility  be  placed  in  a  difficulty.  The 
apparently  little  creature  might  use  such  arguments  about  the 
effect  of  distance,  and  might  appeal  to  such  laws  of  sight  and 
hearing  as  I,  if  unlearned  in  those  things,  might  be  unable 
wholly  to  reject.  But  if  there  were  a  thousand  flies,  all  buzzing, 
to  appearance,  about  the  great  creature ;  and,  to  a  fly,  declaring, 
each  one  for  himself,  that  he  was  bigger  than  the  quadruped ; 
and  all  giving  different  and  frequently  contradictory  reasons  ;  and 
each  one  despising  and  opposing  the  reasons  of  the  others — I 
should  feel  quite  at  my  ease.  I  should  certainly  say,  My  little 
friends,  the  case  of  each  one  of  you  is  destroyed  by  the  rest.  I 
intend  to  show  flies  in  the  swarm,  with  a  few  larger  animals,  for 
reasons  to  be  given. 

In  every  age  of  the  world  there  has  been  an  established  system, 
which  has  been  opposed  from  time  to  time  by  isolated  and  dis- 
sentient reformers.  The  established -system  has  sometimes  fallen, 
slowly  and  gradually :  it  has  either  been  upset  by  the  rising  in- 
fluence of  some  one  man,  or  it  has  been  sapped  by  gradual  change 
of  opinion  in  the  many. 

I  have  insisted  on  the  isolated  character  of  the  dissentients,  as 
an  element  of  the  a  priori  probabilities  of  the  case.  Show  me  a 
schism,  especially  a  growing  schism,  and  it  is  another  thing.  The 
homceopathists,  for  instance,  shall  be,  if  any  one  so  think,  as 


2  A  BUDGET   OF  PARADOXES. 

wrong  as  St.  John  Long ;  but  an  organised  opposition,  supported 
by  the  efforts  of  many  acting  in  concert,  appealing  to  common 
arguments  and  experience,  with  perpetual  succession  and  a  com- 
•mon  seal,  as  the  Queen  says  in  the  charter,  is,  be  the  merit  of  the 
schism  what  it  may,  a  thing  wholly  different  from  the  case  of  the 
isolated  opponent  in  the  mode  of  opposition  to  it  which  reason 
points  out. 

During  the  last  two  centuries  and  a  half,  physical  knowledge 
has  been  gradually  made  to  rest  upon  a  basis  which  it  had  not 
before.  It  has  become  mathematical.  The  question  now  is,  not 
whether  this  or  that  hypothesis  is  better  or  worse  to  the  pure 
thought,  but  whether  it  accords  with  observed  phenomena  in 
those  consequences  which  can  be  shown  necessarily  to  follow  from 
it,  if  it  be  true.  Even  in  those  sciences  which  are  not  yet  under 
the  dominion  of  mathematics,  and  perhaps  never  will  be,  a 
working  copy  of  the  mathematical  process  has  been  made.  This 
is  not  known  to  the  followers  of  those  sciences  who  are  not  them- 
selves mathematicians,  and  who  very  often  exalt  their  horns  against 
the  mathematics  in  consequence.  They  might  as  well  be  squaring 
the  circle,  for  any  sense  they  show  in  this  particular. 

A  great  many  individuals,  ever  since  the  rise  of  the  mathematical 
method,  have,  each  for  himself,  attacked  its  direct  and  indirect 
consequences.  I  shall  not  here  stop  to  point  out  how  the  very 
accuracy  of  exact  science  gives  better  aim  than  the  preceding 
state  of  things  could  give.  I  shall  call  each  of  these  persons  a 
paradoxer,  and  his  system  a  paradox.  I  use  the  word  in  the  old 
sense :  a  paradox  is  something  which  is  apart  from  general 
opinion,  either  in  subject-matter,  method,  or  conclusion. 

Many  of  the  things  brought  forward  would  now  be  called 
crotchets,  which  is  the  nearest  word  we  have  to  old  paradox.  But 
there  is  this  difference,  that  by  calling  a  thing  a  crotchet  we  mean 
to  speak  lightly  of  it ;  which  was  not  the  necessary  sense  of  para- 
dox. Thus  in  the  sixteenth  century  many  spoke  of  the  earth's 
motion  as  the  paradox  of  Copernicus,  who  held  the  ingenuity  of 
that  theory  in  very  high  esteem,  and  some,  I  think,  who  even  in- 
clined towards  it.  In  the  seventeenth  century,  the  depravation 
of  meaning  took  place,  in  England  at  least.  Phillips  says  paradox 
is  '  a  thing  which  seemeth  strange  ' — here  is  the  old  meaning : 
after  a  colon,  he  proceeds — '  and  absurd,  and  is  contrary  to  common 
opinion,'  which  is  an  addition  due  to  his  own  time. 

Some  of  my  readers  are  hardly  inclined  to  think  that  the  word 
paradox  could  once  have  had  no  disparagement  in  its  meaning  ; 
still  less  that  persons  could  have  applied  it  to  themselves.  I 


INTRODUCTORY.  3 

chance  to  have  met  with  a  case  in  point  against  them.  It  is 
Spinoza's  '  Pbilosophia  ScripturaB  Interpres,  Exercitatio  Paradoxa,' 
printed  anonymously  at  Eleutheropolis,  in  1666.  This  place 
was  one  of  several  cities  in  the  clouds,  to  which  the  cuckoos  re- 
sorted who  were  driven  away  by  the  other  birds  ;  that  is,  a  feigned 
place  of  printing,  adopted  by  those  who  would  have  caught  it  if 
orthodoxy  could  have  caught  them.  Thus,  in  1656,  the  works  of 
Socinus  could  only  be  printed  at  Irenopolis.  The  author  deserves 
his  self-imposed  title,  as  in  the  following : — 

Quanto  sane  satius  fuissefc  illam  [Trinitatem]  pro  mysterio  non 
habuisse,  et  Philosophiae  ope,  antequam  quod  esset  statuerent,  secun- 
dum  verse  logices  praecepta  quid  esset  cum  Cl.  Keckermanno  inves- 
tigasse ;  tanto  fervore  ac  labore  in  profundissimas  speluncas  et 
obscurissimos  metaphysicarum  speculationum  atque  fictionum  recessus 
se  recipere  ut  ab  adversariorum.  telis  sententiam  suam  in  tuto  collo- 
carent.  Profecto  magnus  ille  vir  .  .  .  dogma  illud,  quamvis  apud 
theologos  eo  nomine  non  multum  gratiee  iniverit,  ita  ex  immotis 
Philosophies  fundamentis  explicat  ac  demonstrat,  ut  paucis  tantum 
immutatis,  atque  additis,  nihil  amplius  animus  veritate  sincere  deditus 
desiderare  possit. 

This  is  properly  paradox,  though  also  heterodox.  It  supposes, 
contrary  to  all  opinion,  orthodox  and  heterodox,  that  philosophy 
can,  with  slight  changes,  explain  the  Athanasiau  doctrine  so  as  to 
be  at -least  compatible  with  orthodoxy.  The  author  would  stand 
almost  alone,  if  not  quite  ;  and  this  is  what  he  meant.  I  have 
met  with  the  counter-paradox.  I  have  heard  it  maintained  that 
the  doctrine  as  it  stands,  in  all  its  mystery,  is  a  priori  more 
likely  than  any  other  to  have  been  Revelation,  if  such  a  thing 
were  to  be  ;  and  that  it  might  almost  have  been  predicted. 

After  looking  into  books  of  paradoxes  for  more  than  thirty 
years,  and  holding  conversation  with  many  persons  who  have 
written  them,  and  many  who  might  have  done  so,  there  is  one 
point  on  which  my  mind  is  fully  made  up.  The  manner  in 
which  a  paradoxer  will  show  himself,  as  to  sense  or  nonsense,  will 
not  depend  upon  what  he  maintains,  but  upon  whether  he  has  or 
lias  not  made  a  sufficient  knowledge  of  what  has  been  done  by 
others,  especially  as  to  the  mode  of  doing  it,  a  preliminary  to  in-, 
venting  knowledge  for  himself.  That  a  little  knowledge  is  a 
dangerous  thing  is  one  of  the  most  fallacious  of  proverbs.  A 
person  of  small  knowledge  is  in  danger  of  trying  to  make  his 
little  do  the  work  of  more  ;  but  a  person  without  any  is  in  more 
danger  of  making  his  no  knowledge  do  the  work  of  some.  .  Take 
the  speculations  on  the  tides  as  an  instance.  Persons  with  nothing 

"  2 


4  A   BUDGET  OF  PAKADOXES. 

but  a  little  geometry  have  certainly  exposed  themselves  in  their 
modes  of  objecting  to  results  which  require  the  higher  mathe- 
matics to  be  known  before  an  independent  opinion  can  be  formed 
on  sufficient  grounds.  But  persons  with  no  geometry  at  all  have 
done  the  same  thing  much  more  completely. 

There  is  a  line  to  be  drawn  which  is  constantly  put  aside  in  the 
arguments  held  by  parodoxers  in  favour  of  their  right  to  instruct 
the  world.  Most  persons  must,  or  at  least  will,  like  the  lady  in 
Cadogan  Place,1  form  and  express  an  immense  variety  of  opinions 
on  an  immense  variety  of  subjects ;  and  all  persons  must  be  their 
own  guides  in  many  things.  So  far  all  is  well.  But  there  are 
many  who,  in  carrying  the  expression  of  their  own  opinions  beyond 
the  usual  tone  of  private  conversation,  whether  they  go  no  fur- 
ther than  attempts  at  oral  proselytism,  or  whether  they  commit 
themselves  to  the  press,  do  not  reflect  that  they  have  ceased  to 
stand  upon  the  ground  on  which  their  process  is  defensible.  As- 
piring to  lead  others,  they  have  never  given  themselves  the  fair 
chance  of  being  first  led  by  other  others  into  something  better 
than  they  can  start  for  themselves ;  and  that  they  should  first 
do  this  is  what  both  those  classes  of  others  have  a  fair  right  to 
expect.  New  knowledge,  when  to  any  purpose,  must  come  by 
contemplation  of  old  knowledge,  in  every  matter  which  concerns 
thought ;  mechanical  contrivance  sometimes,  not  very  often, 
escapes  this  rule.  All  the  men  who  are  now  called  discoverers,  in 
every  matter  ruled  by  thought,  have  been  men  versed  in  the  minds 
of  their  predecessors,  and  learned  in  what  had  been  before  them. 
There  is  not  one  exception.  I  do  not  say  that  every  man  has 
made  direct  acquaintance  with  the  whole  of  his  mental  ancestry  ; 
many  have,  as  I  may  say,  only  known  their  grandfathers  by  the 
report  of  their  fathers.  But  even  on  ;this  point  it  is  remarkable 
how  many  of  the  greatest  names  in  all  departments  of  knowledge 
have  been  real  antiquaries  in  their  several  subjects.  ., 

I  may  cite,  among  those  who  have  wrought  strongly  upon 
opinion  or  practice  in  science,  Aristotle,  Plato,  Ptolemy,  Euclid, 
Archimedes,  Eoger  Bacon,  Copernicus,  Francis  Bacon,  Ramus, 
Tycho  Brahe,  Galileo,  Napier,  Descartes,  Leibnitz,  Newton, 
Locke.  I  take  none  but  names  known  out  of  their  fields  of  work ; 
and  all  were  learned  as  well  as  sagacious.  I  have  chosen  my 
instances  :  if  any  one  will  undertake  to  show  a  person  of  little  or 
no  knowledge  who  has  established  himself  in  a  great  matter  ot 
pure  thought,  let  him  bring  forward  his  man,  and  we  shall  see. 

This  is  the  true  way  of  putting  off  those  who    plague  others 

1  Mrs.  Wititterly,  in  Nicholas  Nickleby. 


INTRODUCTORY.  5 

with  their  great  discoveries.  The  first  demand  made  should  be 
— Mr.  Moses,  before  I  allow  you  to  lead  me  over  the  Eed  Sea,  I 
must  have  you  show  that  you  are  learned  in  all  the  wisdom  of  the 
Egyptians  upon  your  own  subject.  The  plea  that  it  is  unlikely 
that  this  or  that  unknown  person  should  succeed  where  Newton, 
&c.  have  failed,  or  should  show  Newton,  &c.  to  be  wrong,  is  utterly 
null  and  void.  It  was  worthily  versified  by  Sylvanus  Morgan 
(the  great  herald  who  in  his  '  Sphere  of  Gentry '  gave  coat  armour 
to  '  Gentleman  Jesus,'  as  he  said),  who  sang  of  Copernicus  as 
follows  (1652):— 

If  Tellus  winged  be, 
The  earth  a  motion  round  ; 
Then  much  deceived  are  they 
Who  nere  before  it  found. 
Solomon  was  the  wisest, 
His  wit  nere  this  attained ; 
Cease,  then,  Copernicus, 
Thy  hypothesis  vain. 

Newton,  &c.  were  once  unknown  ;  but  they  made  themselves 
known  by  what  they  knew,  and  then  brought  forward  what  they 
could  do ;  which  I  see  is  as  good  verse  as  that  of  Herald  Sylvanus. 
The  demand  for  previous  knowledge  disposes  of  twenty-nine  cases 
out  of  thirty,  and  the  thirtieth  is  worth  listening  to. 

I  have  not  set  down  Copernicus,  Galileo,  &c.  among  the  para- 
doxers,  merely  because  everybody  knows  them ;  if  my  list  were 
quite  complete,  they  would  have  been  in  it.  But  the  reader  will 
find  Gilbert,  the  great  precursor  of  sound  magnetical  theory ;  and 
several  others  on  whom  no  censure  can  be  cast,  though  some  of 
their  paradoxes  are  inadmissible,  some  unproved,  and  some  capital 
jokes,  true  or  false  :  the  author  of  the  'Vestiges  of  Creation'  is  an 
instance.  I  expect  that  my  old  correspondent,  General  Perronet 
Thompson,  will  admit  that  his  geometry  is  part  and  parcel  of  my 
plan  ;  and  also  that,  if  that  plan  embraced  politics,  he  would 
claim  a  place  for  his  '  Catechism  on  the  Corn  Laws,'  a  work  at  one 
time  paradoxical,  but  which  had  more  to  do  with  the  abolition  of 
the  bread-tax  than  Sir  Robert  Peel. 

My  intention  in  publishing  this  Budget  in  the  Athenceum  is 
to  enable  those  who  have  been  puzzled  by  one  or  two  discoverers 
to  see  hoiv  they  look  in  the  lump.  The  only  question  is,  has  the 
selection  been  fairly  made  ?  To  this  my  answer  is,  that  no  selec- 
tion at  all  has  been  made.  The  books  are,  without  exception, 
those  which  I  have  in  my  own  library  ;  and  I  have  taken  all — I 
mean  all  of  the  kind :  Heaven  forbid  that  I  should  be  supposed 


6  A  BUDGET   OF  PARADOXES. 

to  have  no  other  books  !  But  I  may  have  been  a  collector,  in- 
fluenced in  choice  by  bias  ?  I  answer  that  I  never  have  collected 
books  of  this  sort — that  is,  I  have  never  searched  for  them,  never 
made  up  my  mind  to  look  out  for  this  book  or  that.  I  have 
bought  what  happened  to  come  in  my  way  at  shop  or  auction  ;  I 
have  retained  what  came  in  as  part  of  the  undescribed  portion  of 
miscellaneous  auction  lots ;  I  have  received  a  few  from  friends 
who  found  them  among  what  they  called  their  rubbish ;  and  I 
have  preserved  books  sent  to  me  for  review.  In  not  a  few  in- 
stances the  books  have  been  bound  up  with  others,  unmentioned 
at  the  back ;  and  for  years  I  knew  no  more  I  had  them  than  I 
knew  I  had  Lord  Macclesfield's  speech  on  moving  the  change  of 
Style,  which,  after  I  had  searched  shops,  &c.  for  it  in  vain,  I 
found  had  been  reposing  on  my  own  shelves  for  many  years,  at 
the  end  of  a  summary  of  Leibnitz's  philosophy.  Consequently,  I 
may  positively  affirm  that  the  following  list  is  formed  by  accident 
and  circumstance  alone,  and  that  it  truly  represents  the  casualties 
of  about  a  third  of  a  century.  For  instance,  the  large  proportion 
of  works  on  the  quadrature  of  the  circle  is  not  my  doing  :  it  is 
the  natural  share  of  this  subject  in  the  actual  run  of  events. 

[I  keep  to  my  plan  of  inserting  only  such  books  as  I  possessed 
in  1863,  except  by  casual  notice  in  aid  of  my  remarks.  I  have 
found  several  books  on  my  shelves  which  ought  to  have  been 
inserted.  These  have  their  titles  set  out  at  the  commencement 
of  their  articles,  in  leading  paragraphs  ;  the  casuals  are  without 
this  formality.1] 

Before  proceeding  to  open  the  Budget,  I  say  something  on  niy 
personal  knowledge  of  the  class  of  discoverers  who  square  the 
circle,  upset  Newton,  &c.  I  suspect  I  know  more  of  the  English 
class  than  any  man  in  Britain.  I  never  kept  any  reckoning ;  but 
I  know  that  one  year  with  another — and  less  of  late  years  than  in 
earlier  time — I  have  talked  to  more  than  rive  in  each  year,  giving 
more  than  a  hundred  and  fifty  specimens.  Of  this  I  am  sure, 
that  it  is  my  own  fault  if  they  have  not  been  a  thousand.  Nobody 
knows  how  they  swarm,  except  those  to  whom  they  naturally 
resort.  They  are  in  all  ranks  and  occupations,  of  all  ages  and 
characters.  They  are  very  earnest  people,  and  their  purpose  is 
bonafide  the  dissemination  of  their  paradoxes.  A  great  many — 
the  mass,  indeed — are  illiterate,  and  a  great  many  waste  their 
means,  and  are  in  or  approaching  penury.  But  I  must  say  that 
never,  in  any  one  instance,  has  the  quadrature  of  the  circle,  of 

1  The   brackets  mean  that  the  paragraph   is  substantially  from  some  one  of  the 
Athenceitm  Supplements. — (En.) 


INTRODUCTORY.  7 

the  like,  been  made  a  pretext  for  begging ;  even  to  be  asked  to 
purchase  a  book  is  of  the  very  rarest  occurrence — it  has  happened, 
and  that  is  all. 

These  discoverers  despise  one  another :  if  there  were  the  concert 
among  them  which  there  is  among  foreign  mendicants,  a  man 
who  admitted  one  to  a  conference  would  be  plagued  to  death.  I 
once  gave  something  to  a  very  genteel  French  applicant,  who 
overtook  me  in  the  street,  at  my  own  door,  saying  he  had  picked 
up  my  handkerchief :  whether  he  picked  it  up  in  my  pocket  for 
an  introduction,  I  know  not.  But  that  day  week  came  another 
Frenchman  to  my  house,  and  that  day  fortnight  a  French  lady ; 
both  failed,  and  I  had  no  more  trouble.  The  same  thing  hap- 
pened with  Poles.  It  is  not  so  with  circle-squarers,  &c. :  they 
know  nothing  of  each  other.  Some  will  read  this  list,  and  will 
say  I  am  right  enough,  generally  speaking,  but  that  there  is  an 
"  exception,  if  I  could  but  see  it. 

I  do  not  mean,  by  my  confession  of  the  manner  in  which  I 
have  sinned  against  the  twenty-four  hours,  to  hold  myself  out  as 
accessible  to  personal  explanation  of  new  plans.  Quite  the  con- 
trary :  I  consider  myself  as  having  made  my  report,  and  being 
discharged  from  further  attendance  on  the  subject.  I  will  not, 
from  henceforward,  talk  to  any  squarer  of  the  circle,  trisector  of 
the  angle,  duplicator  of  the  cube,  constructor  of  perpetual  motion, 
subverter  of  gravitation,  stagnator  of  the  earth,  builder  of  the 
universe,  &c.  I  will  receive  any  writings  or  books  which  require 
no  answer,  and  read  them  when  I  please  :  I  will  certainly  preserve 
them — this  list  may  be  enlarged  at  some  future  time. 

There  are  three  subjects  which  I  have  hardly  anything  upon; 
astrology,  mechanism,  and  the  infallible  way  of  winning  at  play. 
I  have  never  cared  to  preserve  astrology.  The  mechanists  make 
models,  and  not  books.  The  infallible  winners — though  I  have 
seen  a  few — think  their  secret  too  valuable,  and  prefer  mutare 
qu<tdrata  rotundis — to  turn  dice  into  coin — at  the  gaming-house  : 
verily  they  have  their  reward. 

I  shall  now  select,  to  the  mystic  number  sev  jn,  instances  of  my 
personal  knowledge  of  those  who  think  they  have  discovered,  in 
illustration  of  as  many  misconceptions. 

1.  Attempt  by  help  of  the  old  philosophy,  the  discoverer  not 
being  in  possession  of  modern  knowledge.  A  poor  schoolmaster, 
in  rags,  introduced  himself  to  a  scientific  friend  with  whom  I  was 
talking,  and  announced  that  he  had  found  out  the  composition  of 
the  sun.  '  How  was  that  done  ?  ' — '  By  consideration  of  the  four 
elements.' — '  What  are  they  ?  ' — '  Of  course,  fire,  air,  earth,  and 


A   BUDGET   OF  PARADOXES. 


water  -'Did  you  not  know  that  air,  earth,  and  water,  have  Ion, 
been  known  to  be  no  elements  at  all,  but  compounds  V_<  Wh 
do  you  mean,  sir  ?     Who  ever  heard  of  such  a  thing  ?  '' 

2.  The  noUonthat  difficulties  are  enigmas,  to  be  overcome  in 
a  moment  by  a  lucky  thought.     A  nobleman  of  very  hET£fc 
now  long  dead,  read  an  article   by  me  on  the  quadrature  in 
early  number  of  the  Penny  Magazine.    He  had,  I  suppose  sc 
recollections  of  geometry.     He  put  pencil  to  paper,  dTw  a     rcle 
and  constructed  what  seemed  likely  to  answer,  and  indeed,  wa  - 
as  he  said-  certain,  if  only  this  bit  were  equal  to  that  ;  wiTh  of 
course  it  was  not      He  forwarded  his  diagram  to  the  Secreta  y 
the  Diffusion  Society,  to  be  handed  to  the  author  of  the  art  Lie 
case  the  difficulty  should  happen  to  be  therein  overcome 

3.  Discovery  at   all  hazards,  to  get  on  in  the  world.     Thirty 
years  ago,  an  officer  of  rank,  just  come  from  foreign  service  and 
trying  for  a  decoration  from  the  Crown,  found  that  his  claim  'were 
of  doubtful  amount  and  was  told  by  a  friend  that  so  and  To  who 

ttn^owt^6  ^  ^.f  df  °nal  Cklm  °f  S™°  «± 

but  that  if  some  clever  fellow  would   mi*  f»,o  *i  • 
light  he  thought  his  affair  m 


e      a  poper 


.    th      ,  '  > 

,  that  though  perhaps  they  were  wrong,  the  advisers 


^     H1S  r6SUIt  WaS  abou       ' 


He  came  to  In  7         ?        ^     H1S  r6SUIt  WaS  about 

ame  to  London,  and  somebody  sent  him  to  me.     Like  manv 

ht  min°d        PUrSUU'  h6  Seemed  t0  ha™  t"™*  «>«  whole  fo^  of 


LO  rfMiiriTirm          TT      l.      i  i  "WH.LU.   uc  UfJtJlJ. 


INTRODUCTORY.  9 

Memoirs,  in  which  were  a  large  number  of  observed  places  of  the 
planets  compared  with  prediction,  and  asked  him  whether  it  could 
be  possible  that  persons  who  did  not  know  the  circle  better  than 
he  had  found  it  could  make  the  calculations,  of  which  I  gave  him 
a  notion,  so  accurately  ?  He  was  perfectly  astonished,  and  took 
the  titles  of  some  books  which  he  said  he  would  read. 

5.  Application  for  the  reward  from  abroad.     Many  years  ago, 
about  twenty-eight,  I  think,  a  Jesuit  came  from  South  America, 
with  a  quadrature,  and  a  cutting  from  a  newspaper,  announcing 
that  a  reward  was  ready  for  the  discovery  in  England.     On  this 
evidence  he  came  over.     After  satisfying  him  that  nothing  had 
ever  been  offered  here,  I  discussed  his  quadrature,  which  was  of 
no  use.     I  succeeded  better  when  I  told  him  of  Richard  White, 
also  a  Jesuit,  and  author  of  a  quadrature  published  before  1648, 
under  the  name  of  Chryscespis,-of  which  I  can  give  no  account, 
having  never  seen  it.     This  White  (Albius)  is  the  only  quad- 
rator  who  was  ever  convinced  of  his  error.     My  Jesuit  was  struck 
by  the  instance,  and  promised  to  read  more  geometry — he  was 
no  Clavius — before  he  published  his  book.     He  relapsed,  how- 
ever, for  I  saw  his  book  advertised  in  a  few  days.     I  may  say,  as 
sufficient  proof  of  my  being  no  collector,  that  I  had  not  the 
curiosity  to  buy  this  book  ;  and  my  friend  the  Jesuit  did  not 
send  me  a  copy,  which  he  ought  to  have  done,  after  the  hour  I 
had  given  him. 

6.  Application  for   the   reward  at  home.       An   agricultural 
labourer  squared  the  circle,  and  brought  the  proceeds  to  London. 
He  left  his  papers  with  me,  one  of  which  was  the  copy  of  a  letter 
to   the   Lord   Chancellor,   desiring   his   Lordship  to  hand  over 
forthwith  100,000^.,  the  amount  of  the  alleged   offer  of  reward. 
He  did  not  go  quite  so  far  as  M.  de  Vausenville,  who,  I  think 
in  1778,  brought  an  action  against  the  Academy  of  Sciences  to 
recover  a  reward  to  which  he  held  himself  entitled.     I  returned 
the  papers,  with  a  note,  stating  that  he  had  not  the  knowledge 
requisite  to  see  in  what  the  problem  consisted.     I  got  for  answer 
a  letter  in  which  I  was  told  that  a  person  who  could  not  see  that 
he  had  done  the  thing  should  '  change   his  business,  and  appro- 
priate his  time  and  attention  to  a  Sunday-school,  to  learn  what 
he  could,  and  keep  the  litle  children  from   durting  their  close.' 
I  also  received  a  letter  from  a  friend  of  the  quadrator,  informing 
me  that  I  knew  his  friend  had  succeeded,  and  had  been  heard  to 
say  so.     These  letters  were  printed — without  the  names   of  the 
writers — for  the  amusement  of  the  readers  of  Notes  and  Queries, 
First  Series,  xii.  57,  and  they  will  appear  again  in  the  sequel. 


10  A   BUDGET   OF   PAKADOXES. 

[There  are  many  who  have  such  a  deep  respect  for  any  attempt 
at  thought  that  they  are  shocked  at  ridicule  even  of  those  who 
have  made  themselves  conspicuous  by  pretending  to  lead  the 
world  in  matters  which  they  have  not  studied.  Among  my 
anonymes  is  a  gentleman  who  is  angry  at  my  treatment  of 
the  '  poor  but  thoughtful '  man  who  is  described  in  my  intro- 
duction as  recommending  me  to  go  to  a  Sunday-school  because  I 
informed  him  that  he  did  not  know  in  what  the  difficulty  of 
quadrature  consisted.  My  impugner  quite  forgets  that  this 
man's  '  thoughtfulness '  chiefly  consisted  in  his  demanding  a 
hundred  thousand  pounds  from  the  Lord  Chancellor  for  his  dis- 
covery; and  I  may  add,  that  his  greatest  stretch  of  invention 
was  finding  out  that  '  the  clergy '  were  the  means  of  his  modest 
request  being  unnoticed.  I  mention  this  letter  because  it  affords 
occasion  to  note  a  very  common  error,  namely,  that  men  unread 
in  their  subjects  have,  by  natural  wisdom,  been  great  benefactors 
of  mankind.  My  critic  says,  '  Shakspeare,  whom  the  Pror  (sic) 
may  admit  to  be  a  wisish  man,  though  an  object  of  contempt  as 
to  learning.  .  .  .'  Shakspeare  an  object  of  contempt  as  to 
learning !  Though  not  myself  a  thoroughgoing  Shakspearean — 
and  adopting  the  first  half  of  the  opinion  given  by  George  III., 
'What!  is  there  not  sad  stuff?  only  one  must  not  say  so' — I 
am  strongly  of  opinion  that  he  throws  out  the  masonic  signs  of 
learning  in  almost  every  scene,  to  all  who  know  what  they  are. 
And  this  over  and  above  every  kind  of  direct  evidence.  First, 
foremost,  and  enough,  the  evidence  of  Ben  Jonson  that  he  had 
'little  Latin  and  less  Greek;'  then  Shakspeare  had  as  much 
Greek  as  Jonson  would  call  some,  even  when  he  was  depreciating. 
To  have  any  Greek  at  all  was  in  those  days  exceptional.  In 
Shakspeare's  youth  St.  Paul's  and  Merchant  Taylors'  schools  were 
to  have  masters  learned  in  good  and  clean  Latin  literature,  and 
also  in  Greek  if  such  may  be  gotten.  When  Jonson  spoke  as 
above,  he  intended  to  put  Shakspeare  low  among  the  learned, 
but  not  out  of  their  pale ;  and  he  spoke  as  a  rival  dramatist,  who 
was  proud  of  his  own  learned  sock ;  and  it  may  be  a  subject  of 
inquiry  how  much  Latin  he  would  call  little.  If  Shakspeare's 
learning  on  certain  points  be  very  much  less  visible  than  Jonson's, 
it  is  partly  because  Shakspeare's  writings  hold  it  in  chemical 
combination,  Jonson's  in  mechanical  aggregation.] 

7.  An  elderly  man  came  to  me,  to  show  me  how  the  universe 
was  created.  There  was  one  molecule,  which  by  vibration  became 
— Heaven  knows  how  ! — the  Sun.  Further  vibration  produced 
Mercury,  and  so  on.  I  suspect  the  nebular  hypothesis  had  got 


INTRODUCTORY.  1 1 

into  the  poor  man's  head  by  reading,  in  some  singular  mixture 
with  what  it  found  there.  Some  modifications  of  vibration  gave 
heat,  electricity,  &c.  I  listened  until  my  informant  ceased  to 
vibrate — which  is  always  the  shortest  way — and  then  said,  '  Our 
knowledge  of  elastic  fluids  is  imperfect.'  '  Sir  ! '  said  he,  '  I 
see  you  perceive  the  truth  of  what  I  have  said,  and  I  will 
reward  your  attention  by  telling  you  what  I  seldom  disclose, 
never,  except  to  those  who  can  receive  my  theory — the  little 
molecule  whose  vibrations  have  given  rise  to  our  solar  system  is 
the  Logos  of  St.  John's  Gospel ! '  He  went  away  to  Dr.  Lardner, 
who  would  not  go  into  the  solar  system  at  all — the  first  molecule 
settled  the  question.  So  hard  upon  poor  discoverers  are  men  of 
science  who  are  not  antiquaries  in  their  subject !  On  leaving, 
he  said,  '  Sir,  Mr.  De  Morgan  received  me  in  a  very  different 
way  ;  he  heard  me  attentively,  and  I  left  him  perfectly  satisfied 
of  the  truth  of  my  system.'  I  have  had  much  reason  to  think 
that  many  discoverers,  of  all  classes,  believe  they  have  convinced 
every  one  who  is  not  peremptory  to  the  verge  of  incivility. 

My  list  is  given  in  chronological  order.  My  readers  will 
understand  that  my  general  expressions,  where  slighting  or 
contemptuous,  refer  to  the  ignorant,  who  teach  before  they 
have  learnt.  In  every  instance,  those  of  whom  I  am  able  to 
speak  with  respect,  whether  as  right  or  wrong,  have  sought 
knowledge  in  the  subject  they  were  to  handle  before  they  com- 
pleted their  speculations.  I  shall  further  illustrate  this  at  the 
conclusion  of  my  list. 

Before  I  begin  the  list,  I  give  prominence  to  the  following 
letter,  addressed  by  me  to  the  Correspondent  of  October  28,  1865. 
Some  of  my  paradoxers  attribute  to  me  articles  in  this  or  that 
journal ;  and  others  may  think — I  know  some  do  think — they 
know  me  as  the  writer  of  reviews  of  some  of  the  very  books 
noticed  here.  The  following  remarks  will  explain  the  way  iu 
which  they  may  be  right,  and  in  whicli  they  may  be  wrong : — 

THE, EDITORIAL  SYSTEM. 

SIR, — I  have  reason  to  think  that  many  persons  Lave  a  very  in- 
accurate notion  of  the  Editorial  system.  What  1  call  by  this  name  has 
grown  up  in  the  last  centenary — a  word  I  may  use  to  signify  the 
hundred  years  now  ending,  arid  to  avoid  the  ambiguity  of  century.  It 
cannot  conveniently  be  explained  by  editors  themselves,  and  edited 
journals  generally  do  not  like  to  say  much  about  it.  In  your  paper 
parhaps,  in  which  editorial  duties  differ  somewhat  from  those  of 
ordinary  journals,  the  common  system  may  be  freely  spoken  of. 


12  A  BUDGET   OF  PARADOXES. 

When  a  reviewed  author,  as  very  often  happens,  writes  to  the 
editor  of  the  reviewing  journal  to  complain  of  what  has  been  said  of 
him,  he  frequently — even  more  often  than  not — complains  of  'your 
reviewer.'  He  sometimes  presumes  that  '  you '  have,  '  through 
inadvertence '  in  this  instance,  '  allowed  some  incompetent  person  to 
lower  the  character  of  your  usually  accurate  pages.'  Sometimes  he 
talks  of  'your  scribe,'  and,  in  extreme  cases,  even  of  '  your  hack.'  All 
this  shows  perfect  ignorance  of  the  journal  system,  except  where  it  is 
done  under  the  notion  of  letting  the  editor  down  easy.  But  the  editor 
never  accepts  the  mercy. 

All  that  is  in  a  journal,  except  what  is  marked  as  from  a  corre- 
spondent, either  by  the  editor  himself  or  by  the  correspondent's  real 
or  fictitious  signature,  is  published  entirely  on  editorial  responsibility, 
as  much  as  if  the  editor  had  written  it  himself.  The  editor,  therefore, 
may  claim,  and  does  claim  and  exercise,  unlimited  right  of  omission, 
addition,  and  alteration.  This  is  so  well  understood  that  the  editor 
performs  his  last  function  on  the  last  revise  without  the  '  contributor ' 
knowing  what  is  done.  The  word  contributor  is  the  proper  one :  it 
implies  that  he  furnishes  materials  without  stating  what  he  furnishes 
or  how  much  of  it  is  accepted,  or  whether  he  be  the  only  contributor. 
All  this  applies  both  to  political  and  literary  journals.  No  editor 
acknowledges  the  right  of  a  contributor  to  withdraw  an  article,  if  he 
should  find  alterations  in  the  proof  sent  to  him  for  correction  which 
would  make  him  wish  that  the  article  should  not  appear.  If  the 
demand  for  suppression  were  made — I  say  nothing  about  what  might 
be  granted  to  request — the  answer  would  be,  '  It  is  not  your  article, 
but  mine ;  I  have  all  the  responsibility ;  if  it  should  contain  a  libel,  I 
could  not  give  you  up,  even  at  your  own  desire.  You  have  furnished 
me  with  materials,  on  the  known  and  common  understanding  that  I 
was  to  use  them  at  my  discretion,  and  you  have  no  right  to  impede  my 
operations  by  making  the  appearance  of  the  article  depend  on  your 
approbation  of  my  use  of  your  materials.' 

There  is  something  to  be  said  for  this  system,  and  something  against 
it — I  mean  simply  on  its  own  merits.  But  the  all-conquering  argu- 
ment in  its  favour  is,  that  the  only  practicable  alternative  is  the 
modern  French  plan  of  no  articles  without  the  signature  of  the  writers. 
I  need  not  discuss  this  plan ;  there  is  no  collective  party  in  favour  of 
it.  Some  may  think  it  is  not  the  only  alternative  ;  they  have  not  pro- 
duced any  intermediate  proposal  in  which  any  dozen  of  persons  have 
concurred.  Many  will  say,  Is  not  all  this,  though  perfectly  correct, 
well  known  to  be  matter  of  form  ?  Is  it  not  practically  the  course  of 
events  that  an  engaged  contributor  writes  the  article,  and  sends  it  to 
the  editor,  who  admits  it  as  written — substantially,  at  least  ?  And  is 
it  not  often  very  well  known,  by  style  and  in  other  ways,  who  it  was 
wrote  the  article  ?  This  system  is  matter  of  form  just  as  much  as 
loaded  pistols  are  matter  of  form  so  long  as  the  wearer  is  not  assailed ; 
but  matter  of  form  takes  the  form  of  matter  in  the  pulling  of  a  trigger, 


INTRODUCTORY.  13 

so  soon  as  the  need  arises.  Editors  aud  contributors  who  can  work 
together  find  each  other  out  by  elective  affinity,  so  that  the  common 
run  of  events  settles  down  into  most  articles  appearing  much  as  they 
are  written.  And  there  are  two  safety-valves  ;  that  is,  when  judicious 
persons  come  together.  In  the  first  place,  the  editor  himself,  when  he 
has  selected  his  contributor,  feels  that  the  contributor  is  likely  to  know 
his  business  better  than  an  editor  can  teach  him  ;  in  fact,  it  is  on 
that  principle  that  the  selection  is  made.  But  he  feels  that  he  is  more 
competent  than  the  writer  to  judge  questions  of  strength  and  of  tone, 
especially  when  the  general  purpose  of  the  journal  is  considered,  of 
which  the  editor  is  the  judge  without  appeal.  An  editor  who  meddles 
with  substantive  matter  is  likely  to  be  wrong,  even  when  he  knows  the 
subject ;  but  one  who  prunes  what  he  deems  excess,  is  likely  to  be 
right,  even  when  he  does  not  know  the  subject.  In  the  second  place, 
a  contributor  knows  that  he  is  supplying  an  editor,  and  learns,  without 
suppressing  truth  or  suggesting  falsehood,  to  make  the  tone  of  his  com- 
munications suit  the  periodical  in  which  they  are  to  appear.  Hence 
it  very  often  arises  that  a  reviewed  author,  who  thinks  he  knows  the 
name  of  his  reviewer,  and  proclaims  it  with  expressions  of  dissatis- 
faction, is  only  wrong  in  supposing  that  his  critic  has  given  all  his 
mind.  It  has  happened  to  myself,  more  than  once,  to  be  announced  as 
the  author  of  articles  which  I  could  not  have  signed,  because  they  did 
not  go  far  enough  to  warrant  my  affixing  my  name  to  them  as  to  a 
sufficient  expression  of  my  own  opinion. 

There  are  two  other  ways  in  which  a  reviewed  author  may  be  wrong 
about  his  critic.  At  editor  frequently  makes  slight  insertions  or 
omissions — I  mean  slight  in  quantity  of  type — as  he  goes  over  the  last 
proof;  this  he  does  in  a  comparative  hurry,  and  it  may  chance  that  he 
does  not  know  the  full  sting  of  his  little  alteration.  The  very  bit  which 
the  writer  of  the  book  most  complains  of  may  not  have  been  seen  by  the 
person  who  is  called  the  writer  of  the  article  until  after  the  appearance 
of  the  journal ;  nay,  if  he  be  one  of  those — few,  I  daresay — who  do  not 
read  their  own  articles,  may  never  have  been  seen  by  him  at  all.  Pos- 
sibly, the  insertion  or  omission  would  not  have  been  made  if  the  editor 
could  have  had  one  minute's  conversation  with  his  contributor.  Some- 
times it  actually  contradicts  something  which  is  allowed  to  remain  in 
another  part  of  the  article ;  and  sometimes,  especially  in  the  case  of 
omission,  it  renders  other  parts  of  the  article  unintelligible.  These  are 
disadvantages  of  the  system,'  and  a  judicious  editor  is  not  very  free 
with  his  nuns  et  alter  pannus.  Next,  readers  in  general,  when  they 
see  the  pages  of  a  journal  with  the  articles  so  nicely  fitting,  and  so 
many  ending  with  the  page  or  column,  have  very  little  notion  of  the 
cutting  and  carving  which  goes  to  the  process.  At  the  very  last 
moment  arises  the  necessity  of  some  trimming  of  this  kind  ;  and  the 
editor,  who  would  gladly  call  the  writer  to  counsel  if  he  could,  is 
obliged  to  strike  out  ten  or  twenty  lines.  He  must  do  his  best,  but  it 
ma  v  chance  that  the  omission  selected  would  take  from  the  writer  the 


14  A  BUDGET   OF  PARADOXES. 

power  of  owning  the  article.  A  few  years  ago,  an  able  opponent  of 
mine  wrote  to  a  journal  some  criticisms  upon  an  article  which  he 
expressly  attributed  to  me.  I  replied  as  if  I  were  the  writer,  which,  in 
a  sense,  I  was.  But  if  any  one  had  required  of  me  an  unmodified  'Yes  ' 
or  '  No '  to  the  question  whether  I  wrote  the  article,  I  must,  of  two 
falsehoods,  have  chosen  '  No  :  '  for  certain  omissions,  dictated  by  the 
necessities  of  space  and  time,  would  have  amounted,  had  my  signature 
been  affixed,  to  a  silent  surrender  of  points  which,  in  my  own  cha- 
racter, I  must  have  strongly  insisted  on,  unless  I  had  chosen  to  admit 
certain  inferences  against  what  I  had  previously  published  in  my  own 
name.  I  may  here  add  that  the  forms  of  journalism  obliged  me  in  this 
case  to  remind  my  opponent  that  it  could  not  be  permitted  to  me,  in 
that  journal,  either  to  acknowledge  or  deny  the  authorship  of  the  articles. 
The  cautions  derived  from  the  above  remarks  are  particularly  wanted 
with  reference  to  the  editorial  comments  upon  letters  of  complaint. 
There  is  often  no  time  to  send  these  letters  to  the  contributor, 
and  even  when  this  can  be  done,  an  editor  is — and  very  properly — 
never  of  so  editorial  a  mind  as  when  he  is  revising  the  comments  of 
a  contributor  upon  an  assailant  of  the  article.  He  is  then  in  a  better 
position  as  to  information,  and  a  more  critical  position  as  to  responsi- 
bility. Of  course,  an  editor  never  meddles,  except  under  notice,  with 
the  letter  of  a  Correspondent,  whether  of  a  complainant,  of  a  casual  in- 
formant, or  of  a  contributor  who  sees  reason  to  become  a  correspondent. 
Omissions  must  sometimes  be  made  when  a  grievance  is  too  highly 
spiced.  It  did  once  happen  to  me  that  a  waggish  editor  made  an  inser- 
tion without  notice  in  a  letter  signed  by  me  with  some  fiction,  which 
insertion  contained  the  name  of  a  friend  of  mine,  with  a  satire  which  I 
did  not  believe,  and  should  not  have  written  if  I  had.  To  my  strong 
rebuke,  he  replied — '  I  know  it  was  very  wrong  ;  but  human  nature 
could  not  resist.'  But  this  was  the  only  occasion  on  which  such  a 
thing  ever  happened  to  me. 

I  daresay  what  I  have  written  may  give  some  of  your  readers  to  under- 
stand some  of  the  pericula  et  commoda  of  modern  journalism.  I  have 
known  men  of  deep  learning  and  science  as  ignorant  of  the  prevailing 
system  as  any  uneducated  reader  of  a  newspaper  in  a  country  town.  I 
may,  perhaps,  induce  some  writers  not  to  be  too  sure  about  this,  that, 
or  the  other  person.  They  may  detect  their  reviewer,  and  they  may  be 
safe  in  attributing  to  him  the  general  matter  and  tone  of  the  article. 
But  about  one  and  another  point,  especially  if  it  be  a  short  and  sting- 
ing point,  they  may  very  easily  chance  to  be  wrong.  It  has  happened 
to  myself,  and  within  a  few  weeks  to  publication,  to  be  wrong  in  two 
ways  in  reading  a  past  article — to  attribute  to  editorial  insertion  what 
was  really  my  own,  and  to  attribute  to  myself  what  was  really  editorial 
insertion. 

What  is  a  man  to  do  who  is  asked  whether  he  wrote  an  article. 
He  may,  of  course,  refuse  to  answer ;  which,  is  regarded  as  an 


INTRODUCTORY.  15 

admission.  He  may  say,  as  Swift  did  to  Serjeant  Bettesworth, 
'  Sir,  when  I  was  a  young  man,  a  friend  of  mine  advised  me, 
whenever  I  was  asked  whether  I  had  written  a  certain  paper,  to 
deny  it ;  and  I  accordingly  tell  you  that  I  did  not  write  it.'  He 
may  say,  as  I  often  do,  when  charged  wit.li  having  invented  a  joke, 
story,  or  epigram,  '  I  wa*nt  all  the  credit  I  can  get,  and  therefore 
I  always  acknowledge  all  that  is  attributed  to  me,  truly  or  not ; 
the  story,  £c.  is  mine.  But  for  serious  earnest,  in  the  matter  of 
imputed  criticism,  the  answer  may  be,  '  That  article  was  of  my 
material,  but  the  editor  has  not  let  it  stand  as  I  gave  it ;  I  cannot 
own  it  as  a  whole.'  He  may  then  refuse  to  be  particular  as  to 
the  amount  of  the  editor's  interference.  Of  this  there  are  two 
extreme  cases.  The  editor  may  have  expunged  nothing  but  a 
qualifying  adverb.  Or  he  may  have  done  as  follows.  We  all 
remember  the  account  of  Adam  which  satirizes  woman,  but 
eulogizes  her  if  every  second  and  third  line  be  transposed.  As 
in — 

Adam  could  find  no  solid  peace 

When  Eve  was  given  him  for  a  mate, 

Till  lie  beheld  a  woman's  face, 
Adam  was  in  a  happy  state. 

If  this  had  been  the  article,  and  a  gallant  editor  had  made  the 
transpositions,  the  author  could  not  with  truth  acknowledge.  If 
the  alteration  were  only  an  omitted  adverb,  or  a  few  things  of  the 
sort,  the  author  could  not  with  truth  deny.  In  all  that  comes 
between,  eveiy  man  must  be  his  own  casuist.  I  stared,  when  I 
was  a  boy,  to  hear  grave  persons  approve  of  Sir  Walter  Scott's 
downright  denial  that  he  was  the  author  of  Waverley,  in  answer 
to  the  Prince  Regent's  downright  question.  If  I  remember 
rightly,  Samuel  Johnson  would  have  approved  of  the  same  course. 
It  is  known  that,  whatever  the  law  gives,  it  also  gives  all  that 
is  necessary  to  full  possession  ;  thus  a  man  whose  land  is  environed 
by  the  land  of  others  has  a  right  of  way  over  the  land  of  these 
others.  By  analogy,  it  is  argued  that  when  a  man  has  a  right  to 
his  secret,  he  has  a  right  to  all  that  is  necessary  to  keep  it,  and 
that  is  not  unlawful.  If,  then,  he  can  only  keep  his  secret  by 
denial,  he  has  a  right  to  denial.  This  I  admit  to  be  an  answer  as 
against  all  men  except  the  denier  himself;  if  conscience  and  self- 
respect  will  allow  it,  no  one  can  impeach  it.  But  the  question 
cannot  be  solved  on  a  case.  That  question  is,  A  lie,  is  it  malum  in 
se,  without  reference  to  meaning  and  circumstances  ?  This  is  a 
question  with  two  sides  to  it.  Cases  may  be  invented  in  which  a 


16  A   BUDGET   OF   PARADOXES. 

lie  is  the  only  way  of  preventing  a  murder,  or  in  which  a  lie  may 
otherwise  save  a  life.  In  these  cases  it  is  difficult  to  acquit,  and 
almost  impossible  to  blame  ;  discretion  introduced,  the  line  be- 
comes very  hard  to  draw. 

I  know  but  one  work  which  has  precisely — as  at  first  appears — 
the  character  and  object  of  my  Budget.  It  is  the  '  Eeview  of  the 
Works  of  the  Eoyal  Society  of  London,'  by  Sir  John  Hill,  M.D. 
(1751  and  1780,  4to.)  This  man  offended  many:  the  Eoyal 
Society,  by  his  work ;  the  medical  profession,  by  inventing  and 
selling  extra-pharmacopceian  doses  ;  Grarrick,  by  resenting  the 
rejection  of  a  play.  So  Grarrick  wrote: 

For  physic  and  farces  his  equal  there  scarce  is  ; 
His  farces  are  physic ;  his  physic  a  farce  is. 

I  have  fired  at  the  Eoyal  Society  and  at  the  medical  profession, 
but  I  have  given  a  wide  berth  to  the  drama  and  its  wits  ;  so 
there  is  no  epigram  out  against  me,  as  yet.  He  was  very  able 
and  very  eccentric.  Dr.  Thomson  (Hist.  Roy.  Soc.~)  says  he  has 
no  humour,  but  Dr.  Thomson  was  a  man  who  never  would  have 
discovered  humour. 

Mr.  Weld  (Hist.  Roy.  Soc.}  backs  Dr.  Thomson,  but  with  a  re- 
markable addition.  Having  followed  his  predecessor  in  observing 
that  the  Transactions  in  Martin  Folkes's  time  have  an  unusual 
proportion  of  trifling  and  puerile  papers,  he  says  that  Hill's  book 
is  a  poor  attempt  at  humour,  and  glaringly  exhibits  the  feelings 
of  a  disappointed  man.  It  is  probable,  he  adds,  that  the  points 
told  with  some  effect  on  the  Society  ;  for  shortly  after  its  publica- 
tion the  Transactions  possess  a  much  higher  scientific  value. 

I  copy  an  account  which  I  gave  elsewhere. 

When  the  Eoyal  Society  was  founded,  the  Fellows  set  to  work 
to  prove  all  things,  that  they  might  hold  fast  that  which  was 
good.  They  bent  themselves  to  the  question  whether  sprats  were 
young  herrings.  They  made  a  circle  of  the  powder  of  a  unicorn's 
horn,  and  set  a  spider  in  the  middle  of  it ;  '  but  it  immediately 
ran  out.'  They  tried  several  times,  and  the  spider  '  once  made 
some  stay  in  the  powder.'  They  enquired  into  Kenelm  Digby's 
sympathetic  powder.  '  Magnetical  cures  being  discoursed  of,  Sir 
Gilbert  Talbot  promised  to  communicate  what  he  knew  of  sym- 
pathetical  cures  ;  and  those  members  who  had  any  of  the  powder 
of  sympathy,  were  desired  to  bring  some  of  it  at  the  next  meeting.' 

June  21,  1661,  certain  gentlemen  were  appointed  '  curators  of 
the  proposal  of  tormenting  a  man  with  the  sympathetic  powder ; ' 
I  cannot  find  any  record  of  the  result.  And  so  they  went  on 


INTRODUCTORY.  1 7 

until  the  time  of  Sir  John  Hill's  satire,  in  1751.  This  once  well- 
known  work  is,  in  my.  judgment,  the  greatest  compliment  the 
Royal  Society  ever  received.  It  brought  forward  a  number  of 
what  are  now  feeble  and  childish  researches  in  the  Philosophical 
Transactions.  It  showed  that  the  inquirers  had  actually  been 
inquiring;  and  that  they  did  not  pronounce  decision  about 
'natural  knowledge'  by  help  of  '  natural  knowledge.'  But  for 
this,  Hill  would  neither  have  known  what  to  assail,  nor  how. 
Matters  are  now  entirely  changed.  The  scientific  bodies  are  far 
too  well  established  to  risk  themselves.  Iblt  qui  zonam  perdidit — 

Let  him  take  castles  who  lias  ne'er  a  gi-oafc. 

These  great  institutions  are  now  without  any  collective  purpose, 
except  that  of  promoting  individual  energy  ;  they  print  for  their 
contributors,  and  guard  themselves  by  a  general  declaration  that 
they  will  not  be  answerable  for  the  things  they  print.  Of  course 
they  will  not  put  forward  anything  for  everybody ;  but  a  writer  of 
a  certain  reputation,  or  matter  of  a  certain  look  of  plausibility  and 
safety,  will  find  admission.  This  is  as  it  should  be  ;  the  pas- 
turer  of  flocks  and  herds  and  the  hunters  of  wild  beasts  are  two 
very  different  bodies,  with  very  different  policies.  The  scientific 
academies  are  what  a  spiritualist  might  call  'publishing  mediums,' 
and  their  spirits  fall  occasionally  into  writing  which  looks  as  if 
minds  in  the  higher  state  were  not  always  impervious  to  nonsense. 

The  following  joke  is  attributed  to  Sir  John  Hill.  I  cannot 
honestly  say  I  believe  it ;  but  it  shows  that  his  contemporaries  did 
not  believe  he  had  no  humour.  Good  stories  are  always  in  some 
sort  of  keeping  with  the  characters  on  which  they  are  fastened. 
•Sir  John  Hill  contrived  a  communication  to  the  Royal  Society 
from  Portsmouth,  to  the  effect  that  a  sailor  had  broken  his  leg  in 
a  fall  from  the  mast-head  ;  that  bandages  and  a  plentiful  applica- 
tion of  tarwater  had  made  him,  in  three  days,  able  to  use  his  leg 
as  well  as  ever.  While  this  communication  was  under  grave 
discussion — it  must  be  remembered  that  many  then  thought  tar- 
water  had  extraordinary  remedial  properties — the  joker  contrived 
that  a  second  letter  should  be  delivered,  which  stated  that  the 
writer  had  forgotten,  in  his  previous  communication,  to  mention 
that  the  leg  was  a  wooden  leg !  Horace  Walpole  told  this  story, 
I  suppose  for  the  first  time  ;  he  is  good  authority  for  the  fact  of 
circulation,  but  for  nothing  more. 

Sir  John  Hill's  book  is  droll  and  cutting  satire.  Dr.  Maty, 
(Sec.  Royal  Society)  wrote  thus  of  it  in  the  Journal  Britannique 
(Feb.  1751),  of  which  he  was  editor: 

c 


18  A  BUDGET   OF  PAEADOXES. 

H  est  facheux  que  cet  ingenieux  Naturaliste,  qui  nous  a  deja  donne 
et  qui  nous  prepare  encore  des  ouvrages  plus  utiles,  empioie  a  cette 
odieuse  tache  une  plume  qu'il  trempe  dans  le  fiel  et  dans  1' absinthe.  II 
est  vrai  que  plusieurs  de  ses  remarques  sont  fondees,  et  qu'a  1'erreur 
qu'il  indique,  il  joint  en  meme  terns  la  correction.  Mais  il  n'est  pas  tou- 
jours  equitable,  et  ne  manque  jamais  d'insulter.  Que  peut  apres  tout 
prouver  son  livre,  si  ce  n'est  que  la  quarante-cinquieme  partie  d'un 
tres-ample  et  tres-utile  Becueil  n'est  pas  exempte  d'erreurs  ?  Devoit- 
il  confondre  avec  des  Ecrivains  superficiels,  dont  la  Liberte  du  Corps  ne 
permet  pas  de  restreindre  la  fertilite,  cette  foule  de  savans  du  Premier 
ordre,  dont  les  Merits  ont  orne  et  ornent  encore  les  Transactions  ?  A-t-il 
oublie  qu'on  j  a  vu  frequemment  les  noms  des  Boyle,  des  Newton, 
des  Halley,  des  De  Moivres,  des  Hans  Sloane,  etc.  ?  Et  qu'on  y  trouve 
encore  ceux  des  Ward,  des  Bradley,  des  Graham,  des  Ellicot,  des  Watson, 
et  d'un  Auteur  que  Mr.  Hill  prefere  a  tous  les  autres,  je  veux  dire  de 
Mr.  Hill  lui-meme  ? 

This  was  the  only  answer  ;  but  it  was  no  answer  at  all.  Hill's 
object  was  to  expose  the  absurdities ;  he  therefore  collected  the 
absurdities.  I  feel  sure  that  Hill  was  a  benefactor  of  the  Royal 
Society ;  and  much  more  than  he  would  have  been  if  he  had 
softened  their  errors  and  enhanced  their  praises.  No  reviewer 
will  object  to  me  that  I  have  omitted  Young,  Laplace,  &c.  But 
then  my  book  has  a  true  title.  Hill  should  not  have  called  his 
a  review  of  the  '  Works.' 

It  was  charged  against  Sir  John  Hill  that  he  had  tried  to 
become  a  Fellow  of  the  Royal  Society  and  had  failed.  This  he 
denied,  and  challenged  the  production  of  the  certificate  which  a 
candidate  always  sends  in,  and  which  is  preserved.  But  perhaps 
he  could  not  get  so  far  as  a  certificate — that  is,  could  not  find  any 
one  to  recommend  him ;  he  was  a  likely  man  to  be  in  such  a 
predicament.  As  I  have  myself  run  foul  of  the  Society  on  some 
little  points,  I  conceive  it  possible  that  I  may  fall  under  a  like 
suspicion.  Whether  I  could  have  been  a  Fellow,  I  cannot  know  ; 
as  the  gentleman  said  who  was  asked  if  he  could  play  the  violin, 
I  never  tried.  I  have  always  had  a  high  opinion  of  the  Society 
upon  its  whole  history.  A  person  used  to  historical  inquiry 
learns  to  look  at  wholes  ;  the  Universities  of  Oxford  and 
Cambridge,  the  College  of  Physicians,  &c.  are  taken  in  all  their 
duration.  But  those  who  are  not  historians — I  mean  not 
possessed  of  the  habit  of  history — hold  a  mass  of  opinions  about 
current  things  which  lead  them  into  all  kinds  of  confusion  when 
they  try  to  look  back.  SN"ot  to  give  an  instance  which  will  offend 
any  set  of  existing  men — this  merely  because  I  can  do  without 
it — let  us  take  the  country  at  large.  Magna  Charta  for  ever  ! 


INTRODUCTORY.  19 

glorious  safeguard  of  our  liberties  !  Nullus  liber  homo  capiatur 
aut  imprisonetur,.  .  .  .  aut  aliquo  modo  destruatur,  nisi  per 
judicium  parium.  .  .  .  Liber  homo;  frank  home;  a  capital 
thing  for  him — but  how  about  the  villeins  ?  Oh,  there  are  none 
noiv !  But  there  were.  Who  cares  for  villains,  or  barbarians,  or 
helots  ?  And  so  England,  and  Athens,  and  Sparta,  were  free 
States  :  all  the  freemen  in  them  were  free.  Long  after  Magna 
Charta,  villains  were  sold  with  their  *  chattels  and  offspring,' 
named  in  that  order.  Long  after  Magna  Charta,  it  was  law  that 
'  Le  Seigniour  poit  rob,  naufrer,  et  chastiser  son  villein  a  son 
volunt,  salve  que  il  ne  poit  luy  maim.' 

The  Eoyal  Society  was  founded  as  a  co-operative  body,  and  co- 
operation was  its  purpose.  The  early  charters,  &c.  do  not  contain 
a  trace  of  the  intention  to  create  a  scientific  distinction,  a  kind 
of  Legion  of  Honour.  It  is  clear  that  the  qualification  was  ability 
and  willingness  to  do  good  work  for  the  promotion  of  natural 
knowledge,  no  matter  in  how  many  persons,  nor  of  what  position 
in  society.  Charles  II.  gave  a  smart  rebuke  for  exclusiveness,  as 
elsewhere  mentioned.  In  time  arose,  almost  of  course,  the  idea 
of  distinction  attaching  to  the  title  ;  and  when  I  first  began 
to  know  the  Society,  it  was  in  this  state.  Gentlemen  of  good 
social  position  were  freely  elected  if  they  were  really  educated 
men  ;  but  the  moment  a  claimant  was  announced  as  resting  on 
his  science,  there  was  a  disposition  to  inquire  whether  he  was 
scientific  enough.  The  maxim  of  the  poet  was  adopted  ;  and 
the  Fellows  were  practically  jdivided  into  Drink-deeps  and 
Taste-nots. 

I  was,  in  early  life,  much  repelled  by  the  tone  taken  by  the 
Fellows  of  the  Society  with  respect  to  their  very  mixed  body.  A 
man  high  in  science — some  thirty-seven  years  ago  (about  1830) — 
gave  me  some  encouragement,  as  he  thought.  '  We  shall  have  you  a 
Fellow  of  the  Royal  Society  in  time,'  said  he.  Umph  !  thought  I : 
for  I  had  thatday  heard  of  some  recent  elections,  the  united  science 
of  which  would  not  have  demonstrated  I.  1,  nor  explained  the  action 
of  a  pump.  Truly  an  elevation  to  look  up  at !  It  came,  further,  to 
my  knowledge  that  the  Royal  Society — if  I  might  judge  by  the 
claims  made  by  very  influential  Fellows — considered  itself  as 
entitled  to  the  best  of  everything :  second-best  being  left  for  the 
newer  bodies.  A  secretary,  in  returning  thanks  for  the  Royal 
at  an  anniversary  of  the  Astronomical,  gave  rather  a  lecture  to 
the  company  on  the  positive  duty  of  all  present  to  send  the  very 
best  to  the  old  body,  and  the  absolute  right  of  the  old  body  to 
expect  it.  An  old  friend  of  mine,  on  a  similar  occasion,  stated  as 

c  2 


20  A  BUDGET   OF  PAEADOXES. 

a  fact  that  the  thing  was  always  done,  as  well  as  that  it  ought  to 
be  done. 

Of  late  years  this  pretension  has  been  made  by  a  President 
of  the  Society.  In  1855,  Lord  Eosse  presented  a  confidential 
memorandum  to  the  Council  on  the  expediency  of  enlarging 
their  number.  He  says,  '  In  a  Council  so  small  it  is  impossible 
to  secure  a  satisfactory  representation  of  the  leading  scientific 
Societies,  and  it  is  scarcely  to  be  expected  that,  under  such  cir- 
cumstances, they  will  continue  to  publish  inferior  papers  while 
they  send  the  best  to  our  Transactio'iis.'1 

And,  again,  with  all  the  Societies  represented  on  the  Council, 
1  even  if  every  Science  had  its  Society,  and  if  they  published  every- 
thing, withholding  their  best  papers  [i.e.  from  the  Eoyal  Society], 
which  they  would  not  be  likely  to  do,  still  there  would  remain  to 
the  Eoyal  Society  .  .  .'  Lord  Eosse  seems  to  imagine  that  the 
minor  Societies  themselves  transfer  their  best  papers  to  the 
Eoyal  Society  ;  that  if,  for  instance,  the  Astronomical  Society 
were  to  receive  from  A.  B.  a  paper  of  unusual  merit,  the  Society 
would  transfer  it  to  the  Eoyal  Society.  This  is  quite  wrong :  any 
preference  of  the  Eoyal  to  another  Society  is  the  work  of  the 
contributor  himself.  But  it  shows  how  well  hafted  is  the  Eoyal 
Society's  claim,  that  a  President  should  acquire  the  notion  that 
it  is  acknowledged  and  acted  upon  by  the  other  Societies,  in  their 
joint  and  corporate  capacities.  To  the  pretension  thus  made  I 
never  could  give  any  sympathy.  When  I  first  heard  Mr.  Christie, 
Sec.  E.  S.,  set  it  forth  at  the  anniversary  dinner  of  the  Astro- 
nomical Society,  I  remembered  the  Baron  in  Walter  Scott — 

Of  Gilbert  the  Galliard  a  heriot  lie  sought, 
Saying,  Give  thy  best  steed  as  a  vassal  ought. 

And  I  remembered  the  answer — 

Lord  and  Earl  though  thou  be,  I  trow 
I  can  rein  Buck's-foot  better  than  thou. 

Fully  conceding  that  the  Eoyal  Society  is  entitled  to  pre- 
eminent rank  and  all  the  respect  due  to  age  and  services,  I 
could  not,  nor  can  I  now,  see  any  more  obligation  in  a  contributor 
to  send  his  best  to  that  Society  than  he  can  make  out  to  be  due 
to  himself.  This  pretension,  in  my  mind,  was  hooked  on,  by 
my  historical  mode  of  viewing  things  already  mentioned,  to  my 
knowledge  of  the  fact  that  the  Eoyal  Society — the  chief  fault, 
perhaps,  lying  with  its  President,  Sir  Joseph  Banks — had  sternly 
set  itself  against  the  formation  of  other  societies  ;  the  Geological 


INTRODUCTORY.  21 

and  Astronomical,  for  instance,  though  it  must  be  added  that 
the  chief  rebels  came  out  of  the  Society  itself.  And  so  a  certain 
not  very  defined  dislike  was  generated  in  my  mind — an  anti- 
aristocratic  affair — to  the  body  which  seemed  to  me  a  little  too 
uplifted.  This  would,  I  daresay,  have  worn  off;  but  a  more 
formidable  objection  arose.  My  views  of  physical  science  gradu- 
ally arranged  themselves  into  a  form  which  would  have  rendered 
F.R.S.,  as  attached  to  my  name,  a  false  representation  symbol. 
The  Royal  Society  is  the  great  fortress  of  general  physics :  and  in 
the  philosophy  of  our  day,  as  to  general  physics,  there  is  some- 
thing which  makes  the  banner  of  the  R.S.  one  under  which  I 
cannot  march.  Everybody  who  saw  the  three  letters  after  my 
name  would  infer  certain  things  as  to  my  mode  of  thought  which 
would  not  be  true  inference.  It  would  take  much  space  to  explain 
this  in  full.  I  may  hereafter,  perhaps,  write  a  budget  of  collected 
results  of  the  a  priori  philosophy,  the  nibbling  at  the  small 
end  of  omniscience,  and  the  effect  it  has  had  on  common  life, 
from  the  family  parlour  to  the  jury-box,  from  the  girls'-school 
to  the  vestry -meeting.  There  are  in  the  Society  those  who 
would,  were  there  no  others,  prevent  my  criticism,  be  its  con- 
clusions true  or  false,  from  having  any  basis ;  but  they  are  in  the 
minority. 

There  is  no  objection  to  be  made  to  the  principles  of  philosophy 
in  vogue  at  the  Society,  when  they  are  stated  as  principles  ;  but 
there  is  an  omniscience  in  daily  practice  which  the  principles 
repudiate.  In  like  manner,  the  most  retaliatory  Christians  have 
a  perfect  form  of  round  words  about  behaviour  to  those  who 
injure  them :  none  of  them  are  as  candid  as  a  little  boy  I  knew, 
who,  to  his  mother's  admonition,  You  should  love  your  enemies, 
answered — Catch  me  at  it ! 

Years  ago,  a  change  took  place  which  would  alone  have  put  a 
sufficient  difficulty  in  the  way.  The  co-operative  body  got  tired 
of  getting  funds  from  and  lending  name  to  persons  who  had  little 
or  no  science,  and  wanted  F.R.S.  to  be  in  every  case  a  Fellow 
Really  Scientific.  Accordingly,  the  number  of  yearly  elections  was 
limited  to  fifteen  recommended  by  the  Council,  unless  the  general 
body  should  choose  to  elect  more  ;  which  it  does  not  do.  The 
election  is  now  a  competitive  examination :  it  is  no  longer — Are  you 
able  and  willing  to  promote  natural  knowledge  ;  it  is — Are  you  one 
of  the  upper  fifteen  of  those  who  make  such  claim.  In  the  list  of 
candidates — a  list  rapidly  growing  in  number — each  year  shows 
from  thirty  to  forty  of  those  whom  Newton  and  Boyle  would  have 
gladly  welcomed  as  fellow-labourers.  And  though  the  rejected 


22  A  BUDGET   OF  PAKADOXES. 

of  one  year  may  be  the  accepted  of  the  next — or  of  the  next  but 
one,  or  but  two,  if  self-respect  will  permit  the  candidate  to  hang 
on — yet  the  time  is  clearly  coming  when  many  of  those  who 
ought  to  be  welcomed  will  be  excluded  for  life,  or  else  shelved  at 
last,  when  past  work,  with  a  scientific  peerage.  Coupled  with 
this  attempt  to  create  a  kind  of  order  of  knighthood  is  'an  ab- 
surdity so  glaring  that  it  should  always  be  kept  before  the  general 
eye.  This  distinction,  this  mark  set  by  science  upon  successful 
investigation,  is  of  necessity  a  class-distinction.  Rowan  Hamilton, 
one  of  the  greatest  names  of  our  day  in  mathematical  science, 
never  could  attach  F.R.S.  to  his  name — he  could  not  afford  it. 
There  is  a  condition  precedent — Four  Red  Sovereigns.  It  is 
four  pounds  a  year,  or — to  those  who  have  contributed  to  the 
Transactions — forty  pounds  down.  This  is  as  it  should  be :  the 
Society  must  be  supported.  But  it  is  not  as  it  should  be  that  a 
kind  of  title  of  honour  should  be  forged,  that  a  body  should  take 
upon  itself  to  confer  distinctions  for  science,  when  it  is  in  the 
background — and  kept  there  when  the  distinction  is  trumpeted — 
that  the  wearer  is  a  man  who  can  spare  four  pounds  a  year.  I 
am  well  aware  that  in  England  a  person  who  is  not  gifted,  either 
by  nature  or  art,  with  this  amount  of  money  power,  is,  with  the 
mass,  a  very  second-rate  sort  of  Newton,  whatever  he  may  be  in 
the  field  of  investigation.  Even  men  of  science,  so  called,  have 
this  feeling.  I  know  that  the  scientific  advisers  of  the  Admiralty, 
who,  years  ago,  received  100£.  a  year  each  for  his  trouble,  were 
sneered  at  by  a  wealthy  pretender  as  '  fellows  to  whom  a  hundred 
a  year  is  an  object.'  Dr.  Thomas  Young  was  one  of  them.  To 
a  bookish  man — I  mean  a  man  who  can  manage  to  collect  books — 
there  is  no  tax.  To  myself,  for  example,  40L  worth  of  books 
deducted  from  my  shelves,  and  the  life-use  of  the  Society's 
splendid  library  instead,  would  have  been  a  capital  exchange. 
But  there  may  be,  and  are,  men  who  want  books,  and  cannot  pay 
the  Society's  price.  The  Council  would  be  very  liberal  in  allow- 
ing their  books  to  be  consulted.  I  have  no  doubt  that  if  a  known 
investigator  were  to  call  and  ask  to  look  at  certain  books,  the 
Assistant-Secretary  would  forthwith  seat  him  with  the  books 
before  him,  absence  of  F.R.S.  not  in  any  wise  withstanding.  But 
this  is  not  like  having  the  right  to  consult  any  book  on  any  day, 
and  to  take  it  away,  if  farther  wanted. 

So  much  for  the  Royal  Society  as  concerns  myself.  I  must  add, 
that  there  is  not  a  spark  of  party  feeling  against  those  who 
wilfully  remain  outside.  The  better  minds  of  course  know  better; 
and  the  smaller  savants  look  complacently  on  the  idea  of  an 


INTRODUCTORY.  23 

outer  world  which  makes  elite  of  them.  I  have  done  such  a 
thing  as  serve  on  a  committee  of  the  Society,  and  report  on  a 
paper :  they  had  the  sense  to  ask,  and  I  had  the  sense  to  see  that 
none  of  my  opinions  were  compromised  by  compliance.  And  I 
will  be  of  any  use  which  does  not  involve  the  status  of  homo  trium 
tiierarum ;  as  I  have  elsewhere  explained,  I  would  gladly  be 
Fautor  Realis  Scientice,  but  I  would  not  be  taken  for  Falsce 
Ra'ioiiis  Sacerdos. 

Nothing  worse  will  ever  happen  to  me  than  the  smile  which 
individuals  bestow  on  a  man  who  does  not  groove.  Wisdom,  like 
religion,  belongs  to  majorities  ;  who  can  wonder  that  it  should  be 
so  thought,  when  it  is  so  clearly  pictured  in  the  New  Testament 
from  one  end  to  the  other  ? 

The  counterpart  of  paradox,  the  isolated  opinion  of  one  or  of 
few,  is  the  general  opinion  held  by  all  the  rest ;  and  the  counter- 
part of  false  and  absurd  paradox  is  what  is  called  the  '  vulgar 
error,'  the  pseudodox.  There  is  one  great  work  on  this  last  subject, 
the  Pseudodoxia  Epidemica  of  Sir  Thomas  Browne,  the  famous 
author  of  the  Religio  Medici:,  it  usually  goes  by  the  name  of 
Browne '  On  Vulgar  Errors '  (1st  ed.  1646  ;  6th,  1672).  A  careful 
analysis  of  this  work  would  show  that  vulgar  errors  are  frequently 
opposed  by  scientific  errors  ;  but  good  sense  is  always  good  sense, 
and  Browne's  book  has  a  vast  quantity  of  it. 

As  an  example  of  bad  philosophy  brought  against  bad  observa- 
tion. The  Amphisbsena  serpent  was  supposed  to  have  two  heads, 
one  at  each  end ;  partly  from  its  shape,  partly  because  it  runs 
backwards  as  well  as  forwards.  On  this  Sir  Thomas  Browne  makes 
the  following  remarks : — 

And  were  there  any  such  species  or  natural  kind  of  animal,  it  would 
be  hard  to  make  good  those  six  positions  of  body  which,  according  to 
the  three  dimensions,  are  ascribed  unto  every  Animal ;  that  is,  infra, 
supra,  ante,  retro,  dextrosum,  sinistrosum :  for  if  (as  it  is  determined) 
that  be  the  anterior  and  upper  part  wherein  the  senses  are  placed,  and 
that  the  posterior  and  lower  part  which  is  opposite  thereunto,  there  is 
no  inferior  or  former  part  in  this  Animal ;  for  the  senses,  being  placed 
at  both  extreams,  doth  make  both  ends  anterior,  which  is  impossible ; 
the  terms  being  Relative,  which  mutually  subsist,  and  are  not  without 
each  other.  And  therefore  this  duplicity  was  ill  contrived  to  place  one 
head  at  both  extreams,  and  had  been  more  tolerable  to  Lave  settled 
three  or  four  at  one.  And  therefore  also  Poets  have  been  more  reason- 
able than  Philosophers,  and  Geryon  or  Cerberus  less  monstrous  than 
Amphitbcentk 

There  may  be  paradox  upon  paradox :  and  there  is  a  good 
instance  in  the  eighth  century  in  the  case  of  Virgil,  an  Irishman, 


24  A   BUDGET   OF  PARADOXES. 

Bishop  of  Salzburg  and  afterwards  Saint,  and  his  quarrels  with 
Boniface,  an  Englishman,  Archbishop  of  Mentz,  also  afterwards 
Saint.  All  we  know  about  the  matter  is,  that  there  exists  a 
letter  of  748  from  Pope  Zachary,  citing  Virgil — then,  it  seems,  at 
most  a  simple  priest,  though  the  Pope  was  not  sure  even  of  that 
— to  Eome  to  answer  the  charge  of  maintaining  that  there  is 
another  world  (mundus)  under  our  earth  (terra),  with  another 
sun  and  another  moon.  Nothing  more  is  known :  the  letter 
contains  threats  in  the  event  of  the  charge  being  true ;  and  there 
history  drops  the  matter.  Since  Virgil  was  afterwards  a  Bishop 
and  a  Saint,  we  may  fairly  conclude  that  he  died  in  the  full 
flower  of  orthodox  reputation.  It  has  been  supposed  —  and  it 
seems  probable — that  Virgil  maintained  that  the  earth  is  peopled 
all  the  way  round,  so  that  under  some  spots  there  are  antipodes ; 
that  his  contemporaries,  with  very  dim  ideas  about  the  roundness 
of  the  earth,  and  most  of  them  with  none  at  all,  interpreted  him 
as  putting  another  earth  under  ours — turned  the  other  way, 
probably,  like  the  second  piece  of  bread-and-butter  in  a  sandwich, 
with  a  sun  and  moon  of  its  own.  In  the  eighth  century  this 
would  infallibly  have  led  to  an  underground  Gospel,  an  under- 
ground Pope,  and  an  underground  Avignon  for  him  to  live  in. 
When,  in  later  times,  the  idea  of  inhabitants  for  the  planets 
was  started,  it  was  immediately  asked  whether  they  had  sinned, 
whether  Jesus  Christ  died  for  them,  whether  their  wine  and  their 
water  could  be  lawfully  used  in  the  sacraments,  &c. 

On  so  small  a  basis  as  the  above  has  been  constructed  a  com- 
panion case  to  the  persecution  of  Galileo.  On  one  side  the 
positive  assertion,  with  indignant  comment,  that  Virgil  was 
deposed  for  antipodal  heresy,  on  the  other,  serious  attempts  at 
justification,  palliation,  or  mystification.  Some  writers  say  that 
Virgil  was  found  guilty ;  others  that  he  gave  satisfactory  expla- 
nation, and  became  very  good  friends  with  Boniface :  for  all 
which  see  Bayle.  Some  have  maintained  that  the  antipodist  was 
a  different  person  from  the  canonised  bishop :  there  is  a  second 
Virgil,  made  to  order.  When  your  shoes  pinch,  and  will  not 
stretch,  always  throw  them  away  and  get  another  pair :  the  same 
with  your  facts.  Baronius  was  not  up  to  the  plan  of  a  substitute  : 
his  commentator  Pagi  (probably  writing  about  1690)  argues  for 
it  in  a  manner  which  I  think  Baronius  would  not  have  approved. 
This  Virgil  was  perhaps  a  slippery  fellow.  The  Pope  says  he 
hears  that  Virgil  pretended  licence  from  him  to  claim  one  of 
some  new  bishoprics  :  this  he  declares  is  totally  false.  It  is  part 
of  the  argument  that  such  a  man  as  this  could  not  have  been 


INTRODUCTOKY.  25 

created  a  Bishop  and  a  Saint:  on  this  point  there  will  be  opinions 
and  opinions.1 

Lactantius,  four  centuries  before,  had  laughed  at  the  antipodes 
in  a  manner  which  seems  to  be  ridicule  thrown  on  the  idea  of  the 
earth's  roundness.      Ptolemy,  without  reference  to  the  antipodes, 
describes  the  extent  of  the  inhabited  part  of  the  globe  in  a  way 
which  shows  that  he  could  have  had  no  objection  to  men  turned 
opposite  ways.     Probably,  in  the  eighth  century,  the  roundness  of 
the  earth  was  matter  of  thought  only  to  astronomers.      It  should 
always  be  remembered,  especially  by  those  who  affirm  persecution 
of  a  true  opinion,  that  but  for  our  knowing  from  Lactantius  that 
the   antipodal  notion  had   been  matter  of  assertion  and  denial 
among  theologians,  we  could  never  have  had  any  great  confidence 
in  Virgil  really  having  maintained  the  simple  theory  of  the  exist- 
ence of  antipodes.     And  even  now  we  are  not  entitled  to  affirm  it 
as  having  historical  proof:  the  evidence  goes  to  Virgil  having 
been  charged   with   very  absurd   notions,  which   it  seems  more 
likely  than   not  were  the   absurd  constructions   which  ignorant 
contemporaries  put  upon  sensible  opinions  of  his. 

One  curious  part  of  this  discussion  is,  that  neither  side  has 
allowed  Pope  Zachary  to  produce  evidence  to  character.      He 
shall  have  been  an  Urban,  say  the  astronomers ;  an  Urban  he 
ought  to  have  been,  say  the  theologians.     What  sort  of  man  was 
Zachary  ?     He  was  eminently  sensible  and  conciliatory  ;  he  con- 
trived to  make  northern  barbarians  hear  reason  in  a  way  which 
puts  him  high  among  that  section  of  the   early  popes  who  had 
the  knack  of  managing  uneducated  swordsmen.     He  kept  the 
peace  in  Italy  to  an  extent  which  historians  mention  with  ad- 
miration.     Even   Bale,  that  .Maharajah  of  pope-haters,   allows 
himself  to  quote  in  favour   of   Zachary,   that  'multa  Papalem 
dignitatem  decentia,  eademque  pra3clara  (scilicet)  opera  confecit.' 
And   this,   though    so  willing   to   find   fault  that,   speaking   of 
Zachary  putting  a  little  geographical  description   of  the   earth 
on  the  portico  of  the  Lateran  Church,  he  insinuates  that  it  was 
intended  to   affirm  that  the  Pope  was  lord  of  the  whole.     Nor 
can  he  say  how  long  Zachary  held  the  see,  except  by  announcing 
his  death  in  752,  '  cum  decem  annis  pestilentia?  sedi  praefuisset.' 

1  An  Irish  antiquary  informs  me  that  Virgil  is  mentioned  in  annals,  at  A.I/.  781,  as 
1  Verghil,  i.e.  the  geometer,  Abbot  of  Achadhbo  [and  Bishop  of  Saltzburg],  died  in 
Germany  in  the  thirteenth  year  of  his  bishoprick.'  No  allusion  is  made  to  his 
opinions ;  but  it  seems  he  was,  by  tradition,  a  mathematician.  The  Abbot  of  Aghabo 
(Queen's  County)  was  canonised  by  Gregory  IX.,  in  1233.  The  story  of  the  second, 
or  scapegoat,  Virgil  would  be  much  damaged  by  the  character  given  to  the  real 
bishop,  if  there  were  anything  in  it  to  dilapidate. 


26  A   BUDGET   OF   PARADOXES. 

There  was  another  quarrel  between  Virgil  and  Boniface  which 
is  an  illustration.  An  ignorant  priest  had  baptised  '  in^nomine 
Patriot,  et  Filia,  et  Spiritua  Sancta.'  Boniface  declared  the 
rite  null  and  void  ;  Virgil  maintained  the  contrary ;  and  Zachary 
decided  in  favour  of  Virgil,  on  the  ground  that  the  absurd  form 
was  only  ignorance  of  Latin,  and  not  heresy.  It  is  hard  to  believe 
that  this  man  deposed  a  priest  for  asserting  the  whole  globe  to 
be  inhabited.  To  me  the  little  information  that  we  have  seems 
to  indicate — but  not  with  certainty — that  Virgil  maintained  the 
antipodes :  that  his  ignorant  contemporaries  travestied  his  theory 
into  that  of  an  underground  cosmos  ;  that  the  Pope  cited  him 
to  Eome  to  explain  his  system,  which,  as  reported,  looked  like 
what  all  would  then  have  affirmed  to  be  heresy ;  that  he  gave 
satisfactory  explanations,  and  was  dismissed  with  honour.  It 
may  be  that  the  educated  Greek  monk,  Zachary,  knew  his 
Ptolemy  well  enough  to  guess  what  the  asserted  heretic  would 
say ;  we  have  seen  that  he  seems  to  have  patronised  geography. 
The  description  of  the  earth,  according  to  historians,  was  a  map  ; 
this  Pope  may  have  been  more  ready  than  another  to  prick  up  his 
ears  at  any  rumour  of  geographical  heresy,  from  hope  of  informa- 
tion. And  Virgil,  who  may  have  entered  the  sacred  presence  as 
frightened  as  Jacquard,  when  Napoleon  I.  sent  for  him  and  said, 
with  a  stern  voice  and  threatening  gesture,  '  You  are  the  man  who 
can  tie  a  knot  in  a  stretched  string,'  may  have  departed  as  well 
pleased  as  Jacquard  with  the  riband  and  pension  which  the  inter- 
view was  worth  to  him. 

A  word  more  about  Baronius.  If  he  had  been  pope,  as  he 
would  have  been  but  for  the  opposition  of  the  Spaniards,  and  if 
he  had  lived  ten  years  longer  than  he  did,  and  if  Clavius,  who 
would  have  been  his  astronomical  adviser,  had  lived  five  years 
longer  than  he  did,  it  is  probable,  nay  almost  certain,  that  the 
great  exhibition,  the  proceeding  against  Galileo,  would  not  have 
furnished  a  joke  against  theology  in  all  time  to  come.  For 
Baronius  was  sensible  and  witty  enough  to  say  that  in  the  Scrip- 
tures the  Holy  Spirit  intended  to  teach  how  to  go  to  Heaven, 
not  how  Heaven  goes ;  and  Clavius,  in  his  last  years,  confessed 
that  the  whole  system  of  the  heavens  had  broken  down,  and 
must  be  mended. 

The  manner  in  which  the  Galileo  case,  a  reality,  and  the 
Virgil  case,  a  fiction,  have  been  hawked  against  the  Eoman  see 
are  enough  to  show  that  the  Pope  and  his  adherents  have  not 
cared  much  about  physical  philosophy.  In  truth,  orthodoxy  has 


INTRODUCTORY.  27 

always  had  other  fish  to  fry.  Physics,  which  in  modern  times 
has  almost  usurped  the  name  philosophy,  in  England  at  least, 
has  felt  a  little  disposed  to  clothe  herself  with  all  the  honours 
of  persecution  which  belong  to  the  real  owner  of  the  name. 
But  the  bishops,  &c.  of  the  middle  ages  knew  that  the  contest 
between  nominalism  and  realism,  for  instance,  had  a  hundred 
times  more  bearing  upon  orthodoxy  than  anything  in  astronomy, 
&c.  A  wrong  notion  about  substance  might  play  the  mischief 
with  transubstantiation. 

The  question  of  the  earth's  motion  was  the  single  point  in 
which  orthodoxy  came  into  real  contact  with  science.  Many 
students  of  physics  were  suspected  of  magic,  many  of  atheism  :  but, 
stupid  as  the  mistake  may  have  been,  it  was  bond  fide  the  magic  or 
the  atheism,  not  the  physics,  which  was  assailed.  In  the  astro- 
nomical case  it  was  the  very  doctrine,  as  a  doctrine,  indepen- 
dently of  consequences,  which  was  the  corpus  delicti :  and  this 
because  it  contradicted  the  Bible.  And  so  it  did ;  for  the  stability 
of  the  earth  is  as  clearly  assumed  from  one  end  of  the  Old  Testa- 
ment to  the  other  as  the  solidity  of  iron.  Those  who  take  the 
Bible  to  be  totidem,  verbis  dictated  by  the  God  of  Truth  can 
refuse  to  believe  it;  and  they  make  strange  reasons.  They 
undertake,  a  prioi*i,  to  settle  Divine  intentions.  The  Holy  Spirit 
did  not  mean  to  teach  natural  philosophy :  this  they  know  before- 
hand ;  or  else  they  infer  it  from  finding  that  the  earth  does  move, 
and  the  Bible  says  it  does  not.  Of  course,  ignorance  apart,  every 
word  is  truth,  or  the  writer  did  not  mean  truth.  But  this  puts 
the  whole  book  on  its  trial :  for  we  never  can  find  out  what  the 
writer  meant,  until  we  otherwise  find  out  what  is  true.  Those 
who  like  may,  of  course,  declare  for  an  inspiration  over  which 
they  are  to  be  viceroys  ;  but  common  sense  will  either  accept 
verbal  meaning  or  deny  verbal  inspiration. 


28  A  BUDGET  OF  PARADOXES. 


Questiones  Morales,  folio,  1489  [Paris].     By  T.  Buridan. 

This  is  the  title  from  the  Hartwell  Catalogue  of  Law  Books.  I 
suppose  it  is  what  is  elsewhere  called  the  '  Commentary  on  the 
Ethics  of  Aristotle,'  printed  in  1489.  Buridan  (died  about  1358) 
is  the  creator  of  the  famous  ass  which,  as  Burdin's  ass,  was  cur- 
rent in  Burgundy,  perhaps  is,  as  a  vulgar  proverb.  Spinoza  says 
it  was  a  jenny  ass,  and  that  a  man  would  not  have  been  so  foolish  ; 
but  whether  the  compliment  is  paid  to  human  or  to  masculine 
character  does  not  appear — perhaps  to  both  in  one.  The  story 
told  about  the  famous  paradox  is  very  curious.  The  Queen  of 
France,  Joanna  or  Jeanne,  was  in  the  habit  of  sewing  her  lovers 
up  in  sacks,  and  throwing  them  into  the  Seine ;  not  for  blab- 
bing, but  that  they  might  not  blab — certainly  the  safer  plan. 
Buridan  was  exempted,  and,  in  gratitude,  invented  the  sophism. 
What  it  has  to  do  with  the  matter  has  never  been  explained. 
Assuredly  qui  facit  per  alium  facit  per  se  will  convict  Buridan 
of  prating.  The  argument  is  as  follows,  and  is  seldom  told  in 
full.  Buridan  was  for  free-will — that  is,  will  which  determines 
conduct,  let  motives  be  ever  so  evenly  balanced.  An  ass  is  equally 
pressed  by  hunger  and  by  thirst ;  a  bundle  of  hay  is  on  one  side, 
a  pail  of  water  on  the  other.  Surely,  you  will  say,  he  will  not  be 
ass  enough  to  die  for  want  of  food  or  drink  ;  he  will  then  make 
a  choice — that  is,  will  choose  between  alternatives  of  equal  force. 
The  problem  became  famous  in  the  schools  ;  some  allowed  the 
poor  donkey  to  die  of  indecision ;  some  denied  the  possibility  of 
the  balance,  which  was  no  answer  at  all. 

The  following  question  is  more  difficult,  and  involves  free-will 
to  all  who  answer — '  Which  you  please.'  If  the  northern  hemisphere 
were  land,  and  all  the  southern  hemisphere  water,  ought  we  to 
call  the  northern  hemisphere  an  island,  or  the  southern  hemisphere 
a  lake  ?  Both  the  questions  would  be  good  exercises  for  paradoxers 
who  must  be  kept  employed,  like  Michael  Scott's  devils.  The 
wizard  knew  nothing  about  squaring  the  circle,  &c.,  so  he  set 
them  to  make  ropes  out  of  sea  sand,  which  puzzled  them.  Stupid 
devils  !  much  of  our  glass  is  sea  sand,  and  it  makes  beautiful 
thread.  Had  Michael  set  them  to  square  the  circle  or  to  find 
a  perpetual  motion,  he  would  have  done  his  work  much  better. 
But  all  this  is  conjecture :  who  knows  that  I  have  not  hit  on  the 
very  plan  he  adopted  ?  Perhaps  the  whole  race  of  paradoxers 
on  hopeless  subjects  are  Michael's  subordinates,  condemned  to 
transmigration  after  transmigration,  until  their  task  is  done. 


THE   BUDGET   OPENED— BURIDAN.  29 

The  above  was  not  a  bad  guess.  A  little  after  the  time  when 
the  famous  Pascal  papers  were  produced,  I  came  into  possession 
of  a  correspondence  which,  but  for  these  papers,  I  should  have 
held  too  incredible  to  be  put  before  the  world.  But  when  one 
sheep  leaps  the  ditch,  another  will  follow  :  so  I  gave  the  following- 
account  in  the  Athenceum  of  October  5,  1867  : — 

The  recorded  story  is  that  Michael  Scott,  being  bound  by  contract 
to  procure  perpetual  employment  for  a  number  of  young  demons,  was 
worried  out  of  his  life  in  inventing  jobs  for  them,  until  at  last  he  set 
them  to  make  ropes  out  of  sea  sand,  which  they  never  could  do.  We 
have  obtained  a  very  curious  correspondence  between  the  wizard 
Michael  and  his  demon-slaves  ;  but  we  do  not  feel  at  liberty  to  say  how 
it  came  into  our  hands.  We  much  regret  that  we  did  not  receive  it 
in  time  for  the  British  Association.  It  appears  that  the  story,  true  as 
far  as  it  goes,  was  never  finished.  The  demons  easily  conquered  the 
rope  difficulty,  by  the  simple  process  of  making  the  sand  into  glass, 
and  spinning  the  glass  into  thread,  which  they  twisted.  Michael, 
thoroughly  disconcerted,  hit  upon  the  plan  of  setting  some  to  square 
the  circle,  others  to  find  the  perpetual  motion,  &c.  He  commanded 
each  of  them  to  transmigrate  from  one  human  body  into  another,  until 
their  tasks  were  done.  This  explains  the  whole  succession  of  cyclo- 
meters, and  all  the  heroes  of  the  Budget.  Some  of  this  correspondence 
is  very  recent ;  it  is  much  blotted,  and  we  are  not  quite  sure  of  its 
meaning  :  it  is  full  of  figurative  allusions  to  driving  something  illegible 
down  a  steep  into  the  sea.  It  looks  like  a  humble  petition  to  be 
allowed  some  diversion  iu  the  intervals  of  transmigration ;  and  the 

answer  is — 

Rumpat  et  serpens  iter  institutum, 

— a  line  of  Horace,  which  the  demons  interpret  as  a  direction  to  come 
athwart  the  proceedings  of  the  Institute  by  a  sly  trick.  Until  we  saw 
this,  we  were  suspicious  of  M.  Libri  :  the  unvarying  blunders  of  the 
correspondence  look  like  knowledge.  To  be  always  out  of  the  road 
requires  a  map  :  genuine  ignorance  occasionally  lapses  into  truth.  We 
thought  it  possible  M.  Libri  might  have  played  the  trick  to  show  how 
easily  the  French  are  deceived  ;  but  with  our  present  information,  our 
minds  are  at  rest  on  the  subject.  We  see  M.  Chasles  does  not  like  to 
avow  the  real  source  of  information :  lie  will  not  confess  himself  a 
spiritualist. 


30  A  BUDGET  OF  PARADOXES. 

Philo  of  Gradara  is  asserted  by  Montucla,  on  the  authority  of 
Eutocius,  the  commentator  on  Archimedes,  to  have  squared  the 
circle  within  the  ten-thousandth  part  of  a  unit,  that  is,  to  four 
places  of  decimals.  A  modern  classical  dictionary  represents  it  as 
done  by  Philo  to  ten  thousand  places  of  decimals.  Lacroix  com- 
ments on  Montucla  to  the  effect  that  myriad  (in  Greek  ten  thou- 
sand] is  here  used  as  we  use  it,  vaguely,  for  an  immense  number. 
On  looking  into  Eutocius,  I  find  that  not  one  definite  word  is 
said  about  the  extent  to  which  Philo  carried  the  matter.  I  give 
a  translation  of  the  passage  : — 

We  ought  to  know  that  Apollonius  Pergseus,  in  his  Ocytocium  [this 
work  is  lost],  demonstrated  the  same  by  other  numbers,  and  came 
nearer,  which  seems  more  accurate,  but  has  nothing  to  do  with 
Archimedes ;  for,  as  before  said,  he  aimed  only  at  going  near  enough 
for  the  wants  of  life.  Neither  is  Porus  of  Nicaea  fair  when  he  takes 
Archimedes  to  task  for  not  giving  a  line  accurately  equal  to  the 
circumference.  He  says  in  his  Cerii  that  his  teacher,  Philo  of  Gadara, 
had  given  a  more  accurate  approximation  (etc  tucpifiemipove  opiflyuovg 
ayayetv)  than  that  of  Archimedes,  or  than  7  to  22.  But  all  these  [the 
rest  as  well  as  Philo]  miss  the  intention.  They  multiply  and  divide  by 
tens  of  thousands,  which  no  one  can  easily  do,  unless  he  be  versed  in 
the  logistics  [fractional  computation]  of  Magnus  [now  unknown]. 

Montucla,  or  his  source,  ought  not  to  have  made  this  mistake. 
He  had  been  at  the  Greek  to  correct  Philo  Gadetanus,  as  he  had 
often  been  called,  and  he  had  brought  away  and  quoted  airo 
TaSapwv.  Had  he  read  two  sentences  further,  he  would  have 
found  the  mistake. 

We  here  detect  a  person  quite  unnoticed  hitherto  by  the 
moderns,  Magnus  the  arithmetician.  The  phrase  is  ironical ;  it 
is  as  if  we  should  say, '  To  do  this  a  man  must  be  deep  in  Cocker.' 
Accordingly,  Magnus,  Baveme,  and  Cocker,  are  three  personifica- 
tions of  arithmetic ;  and  there  may  be  more. 

Aristotle,  treating  of  the  category  of  relation,  denies  that  the 
quadrature  has  been  found,  but  appears  to  assume  that  it  can  be 
done.  Boethius,  in  his  comment  on  the  passage,  says  that  it  has 
been  done  since  Aristotle,  but  that  the  demonstration  is  too  long 
for  him  to  give.  Those  who  have  no  notion  of  the  quadrature 
question  may  look  at  the  English  Cyclopaedia,  art.  'Quadrature 
of  the  Circle.' 


EAKLY  CIRCLE  SQUARERS.  31 


Tetragonismus.  Id  est  circuli  quadratura  per  Campanula, 
Archimedem  Syracusanum,  atque  Boetium  mathematicse  per- 
spicacissimos  adinventa. — At  the  end,  Impressum  Venetiis  per 
loan.  Bapti.  Sessa.  Anno  ab  incarnatione  Domini,  1503.  Die 
28  Augusti. 

This  book  has  never  been  noticed  in  the  history  of  the  subject, 
and  I  cannot  find  any  mention  of  it.  The  quadrature  of  Campanus 
takes  the  ratio  of  Archimedes,  7  to  22,  to  be  absolutely  correct ; 
the  account  given  of  Archimedes  is  not  a  translation  of  his  book  ; 
and  that  of  Boetius  has  more  than  is  in  BoetAius.  This  book 
must  stand,  with  the  next,  as  the  earliest  in  print  on  the  subject, 
until  further  showing :  Murhard  and  Kastner  have  nothing  so 
early.  It  is  edited  by  Lucas  Gauricus,  who  has  given  a  short 
preface.  Luca  Gaurico,  Bishop  of  Civita  Ducale,  an  astrologer 
of  astrologers,  published  this  work  at  about  thirty  years  of  age, 
and  lived  to  eighty-two.  His  works  are  collected  in  folios,  but  I 
do  not  know  whether  they  contain  this  production.  The  poor  fellow 
could  never  tell  his  own  fortune,  because  his  father  neglected  to 
note  the  hour  and  minute  of  his  birth.  But  if  there  had  been 
anything  in  astrology,  he  could  have  worked  back,  as  Adams  and 
Leverrier  did  when  they  caught  Neptune  :  at  sixty  he  could  have 
examined  every  minute  of  his  day  of  birth,  by  the  events  of  his 
life,  and  so  would  have  found  the  right  minute.  He  could  then 
have  gone  on,  by  rules  of  prophecy.  Gauricus  was  the  mathe- 
matical teacher  of  Joseph  Scaliger,  who  did  him  no  credit,  as  we 
shall  see. 

In    hoc    opere   contenta  Epitome Liber    de    quadratura 

Circuli Paris,  1503,  folio. 

The  quadrator  is  Charles  Bovillus,  who  adopted  the  views  of 
Cardinal  Cusa,  presently  mentioned.  Montucla  is  hard  on  his 
compatriot,  who,  he  says,  was  only  saved  from  the  laughter  of 
geometers  by  his  obscurity.  Persons  must  guard  against  most 
historians  of  mathematics  in  one  point :  they  frequently  attribute 
to  Jns  oivn  age  the  obscurity  which  a  writer  has  in  their  own  time. 
This  tract  was  printed  by  Henry  Stephens,  at  the  instigation  of 
Faber  Stapulensis,  and  is  recorded  by  Dechales,  &c.  It  was  also 
introduced  into  the  'Margarita  Philosophica'  of  1815,  in  the 
same  appendix  with  the  new  perspective  from  Viator.  This  is  not 
extreme  obscurity,  by  any  means.  The  quadrature  deserved  it ; 
but  that  is  another  point. 


32  A   BUDGET   OF   PARADOXES. 

It  is  stated  by  Montucla  that  Bovillus  makes  TT  —  VW.  But 
Montucla  cites  a  work  of  1507,  Introductorium  Geometricum., 
which  I  have  never  seen.  He  finds  in  it  an  account  which 
Bovillus  gives  of  the  quadrature  of  the  peasant  labourer,  and 
describes  it  as  agreeing  with  his  own.  But  the  description  makes 
TT  =  3£,  which  it  thus  appears  Bovillus  could  not  distinguish 
from  V 10.  It  seems  also  that  this  3£,  about  which  we  shall  see 
so  much  in  the  sequel,  takes  its  rise  in  the  thoughtful  head  of  a 
poor  labourer.  It  does  him  great  honour,  being  so  near  the  truth, 
and  he  having  no  means  of  instruction.  In  our  day,  when  an 
ignorant  person  chooses  to  bring  his  fancy  forward  in  opposition 
to  demonstration  which  he  will  not  study,  he  is  deservedly 
laughed  at. 

Mr.  James  Smith,  of  Liverpool — hereinafter  notorified — attri- 
butes the  first  announcement  of  3^  to  M.  Joseph  Lacornme,  a 
French  well-sinker,  of  whom  he  gives  the  following  account  :— 

In  the  year  1836,  at  which  time  Lacomme  could  neither  read  nor 
write,  he  had  constructed  a  circular  reservoir  and  wished  to  know  the 
quantity  of  stone  that  would  be  required  to  pave  the  bottom,  and  for 
this  purpose  called  on  a  professor  of  mathematics.  On  putting  his 
question  and  giving  the  diameter,  he  was  surprised  at  getting  the 
following  answer  from  the  Professor — '  Qu'il  lui  e'ait  impossible  de  le  lid 
dire  au  juste,  attendu  quepersonne  n'avait  encore  pu  trouver  d'une  maniere 
exacte  le  rapport  de  la  circonference  au  diametre.'  From  this  he  was 
led  to  attempt  the  solution  of  the  problem.  His  first  process  was 
purely  mechanical,  and  he  was  so  far  convinced  he  had  made  the  dis- 
covery that  he  took  to  educating  himself,  and  became  an  expert 
arithmetician,  and  then  found  that  arithmetical  results  agreed  with  his 
mechanical  experiments.  He  appears  to  have  eked  out  a  bare  existence 
for  many  years  by  teaching  arithmetic,  all  the  time  struggling  to  get  a 
hearing  from  some  of  the  learned  societies,  but  without  success.  In 
the  year  1855  he  found  his  way  to  Paris,  where,  as  if  by  accident,  he 
made  the  acquaintance  of  a  young  gentleman,  son  of  M.  Winter,  a 
commissioner  of  police,  and  taught  him  his  peculiar  methods  of  calcu- 
lation. The  young  man  was  so  enchanted  that  he  strongly  recom- 
mended Lacomme  to  his  father,  and  subsequently  through  M.  Winter 
he  obtained  an  introduction  to  the  President  of  the  Society  of  Arts  and 
Sciences  of  Paris.  A  committee  of  the  society  was  appointed  to 
examine  and  report  upon  his  discovery,  and  the  society  at  its  seance 
of  March  17,  1856,  awarded  a  silver  medal  of  the  first  class  to 
M.  Joseph  Lacomme  for  his  discovery  of  the  true  ratio  of  diameter 
to  circumference  in  a  circle.  He  subsequently  received  three  other 
medals  from  other  societies.  While  writing  this  I  have  his  likeness 
before  me,  with  his  medals  on  his  breast,  which  stands  as  a  frontispiece 


NICHOLAS  OF  CUSA— AGRIPPA.  33 

to  a  short  biography  of  this  extraordinary  man,  for  which  I  am  in- 
debted to  the  gentleman  who  did  me  the  honour  to  publish  a  French 
translation  of  the  pamphlet  I  distributed  at  the  meeting  of  the  British 
Association  for  the  Advancement  of  Science,  at  Oxford,  in  1860. — 
Correspo-ndent,  May  3,  1866. 

My  inquiries  show  that  the  story  of  the  medals  is  not  incredible. 
There  are  at  Paris  little  private  societies  which  have  not  so  much 
claim  to  be  exponents  of  scientific  opinion  as  our  own  Mechanics' 
Institutes.  Some  of  them  were  intended  to  give  a  false  lustre :  as 
the  *  Institut  Historique,'  the  members  of  which  are  '  Membre  de 
1'Institut  Historique.'  That  M.  Lacomme  should  have  got  four 
medals  from  societies  of  tbis  class  is  very  possible  :  that  be  should 
have  received  one  from  any  society  at  Paris  wbicb  bas  tbe  least 
claim  to  give  one  is  as  yet  simply  incredible. 

Nicolai  de  Cusa  Opera  Omnia.     Venice,  1514.     3  vols.  folio. 

The  real  title  is  'Haec  accurata  recognitio  trium  voluminum 
operum  clariss.  P.  Nicolai  Cusse  .  ,  .  proximo  sequens  pagina 
monstrat.'  Cardinal  Cusa,  wbo  died  in  1464,  is  one  of  tbe  earliest 
modern  attempters.  His  quadrature  is  found  in  tbe  second 
volume,  and  is  now  quite  unreadable.  In  these  early  days  every 
quadrator  found  a  geometrical  opponent,  wbo  finished  him. 
Eegiomontanus  did  tbis  office  for  tbe  Cardinal. 

De  Occulta  Philosophia  libri  III.     By  Henry  Cornelius  Agrippa. 

Lyons,  1550,  8vo. 
De  incertitudine  et  vanitate  scientiarum.    By  the  same.     Cologne, 

1531,  8vo. 

Tbe  first  editions  of  these  works  were  of  1530,  as  well  as  I  can 
make  out;  but  tbe  first  was  in  progress  in  1510.     In  the  second 
work  Agrippa  repents  of  having  wasted  time  on  the  magic  of  tbe 
first ;  but  all  those  who  actually  deal  witb  demons  are  destined 
to  eternal  fire  witb  Jamnes  and  Mambres   and    Simon  Magus. 
This  means,  as  is  tbe  fact,  that  his  occult  philosophy  did  not  actu- 
ally enter  upon  black  magic,  but  confined  itself  to  the  power  of 
tbe  stars,  of  numbers,  &c.     The  fourth  book,  which  appeared  after 
tbe  deatb  of  Agrippa,  and  really  concerns  dealing  witb  evil  spirits, 
is  undoubtedly  spurious.     It  is  very  difficult  to  make  out  what 
Agrippa  really  believed  on  tbe  subject.     I  have  introduced  his 
books  as  the  most  marked  specimens  of  treatises  on  magic,  a 
paradox  of  our  day,  though  not  far  from  orthodoxy  in  bis ;    and 
bere  I  should  have  ended  my  notice,  if  I  had  not  casually  found 
something  more  interesting  to  tbe  reader  of  our  day. 

D 


34  A  BUDGET   OF  PARADOXES. 

Walter  Scott,  it  is  well  known,  was  curious  on  all  matters 
connected  with  magic,  and  has  used  them  very  widely.  But  it  is 
hardly  known  how  much  pains  he  has  taken  to  be  correct,  and  to 
give  the  real  thing.  The  most  decided  detail  of  a  magical  pro- 
cess which  is  found  in  his  writings  is  that  of  Dousterswivel  in 
'  The  Antiquary  ' ;  and  it  is  obvious,  by  his  accuracy  of  process, 
that  he  does  not  intend  the  adept  for  a  mere  impostor,  but  for 
one  who  had  a  lurking  belief  in  the  efficacy  of  his  own  processes, 
coupled  with  intent  to  make  a  fradulent  use  of  them.  The 
materials  for  the  process  are  taken  from  Agrippa.  I  first  quote 
Mr.  Dousterswivel : 

...  I  take  a  silver  plate  when  she  [the  moon]  is  in  her  fifteenth 
mansion,  which  mansion  is  in  de  head  of  Libra,  and  I  engrave  upon  one 
side  de  worts  Schedbarschemoth  Schartachan  \_ch  should  be  t~\ — dat  is, 
de  Intelligence  of  de  Intelligence  of  de  moon — and  I  make  his  picture 
like  a  flying  serpent  with  a  turkey-cock's  head — vary  well — Then  upon 
this  side  I  make  de  table  of  de  moon,  which  is  a  square  of  nine, 
multiplied  into  itself,  with  eighty-one  numbers  [nine]  on  every  side, 
and  diameter  nine.  .  .  . 

In  the'De  Occulta  Philosophia,'  p.  290,  we  find  that  the 
fifteenth  mansion  of  the  moon  incipit  capite  Librae,  and  is  good 
pro  extrahendis  thesauris,  the  object  being  to  discover  hidden 
treasure.  In  p.  246,  we  learn  that  a  silver  plate  must  be  used 
with  the  moon.  In  p.  248,  we  have  the  words  which  denote  the 
Intelligence,  &c.  But,  owing  to  the  falling  of  a  number  into  a 
wrong  line,  or  the  misplacement  of  a  line,  one  or  other — which 
takes  place  in  all  the  editions  I  have  examined — Scott  has,  sad 
to  say,  got  hold  of  the  wrong  words  ;  he  has  written  down  the 
demon  of  the  demons  of  the  moon.  Instead  of  the  gibberish 
above,  it  should  have  been  Malcha  betharsisim  hed  beruah  sche- 
hakim.  In  p.  253,  we  have  the  magic  square  of  the  moon,  with 
eighty-one  numbers,  and  the  symbol  for  the  Intelligence,  which 
Scott  likens  to  a  flying  serpent  with  a  turkey-cock's  head.  He 
was  obliged  to  say  something ;  but  I  will  stake  my  character — 
and  so  save  a  woodcut — on  the  scratches  being  more  like  a  pair 
of  legs,  one  shorter  than  the  other,  without  a  body,  jumping  over 
a  six-barred  gate  placed  side  uppermost.  Those  who  thought 
that  Scott  forged  his  own  nonsense,  will  henceforth  stand  corrected. 
As  to  the  spirit  Peolphan,  &c.,  no  doubt  Scott  got  it  from  the 
authors  he  elsewhere  mentions,  Nicolaus  Remigius  and  Petrus 
Thyracus  ;  but  this  last  word  should  be  Thyraeus. 

The  tendency  of  Scott's  mind  towards  prophecy  is  very  marked, 


OEONTIUS   FINAEUS-URSUS.  35 

and  it  is  always  fulfilled.  Hyder,  in  his  disguise,  calls  out  to 
Tippoo — '  Cursed  is  the  prince  who  barters  justice  for  lust ;  he 
shall  die  in  the  gate  by  the  sword  of  the  stranger.'  Tippoo  was 
killed  in  a  gateway  at  Seringapatam. 

Orontii  Finaei.  .   .  Quadrature  Circuli.     Paris,  1544,  4to. 

Orontius  squared  the  circle  out  of  all  comprehension ;  but  he 
was  killed  by  a  feather  from  his  own  wing.  His  former  pupil, 
John  Buteo,  the  same  who — I  believe  for  the  first  time — calculated 
the  question  of  Noah's  ark,  as  to  its  power  to  hold  all  the  animals 
and  stores,  unsquared  him  completely.  Orontius  was  the  author 
of  very  many  works,  and  died  in  1555.  Among  the  laudatory 
verses  which,  as  was  usual,  precede  this  work,  there  is  one  of  a 
rare  character  :  a  congratulatory  ode  to  the  wife  of  the  author. 
The  French  now  call  this  writer  Oronce  Finee  ;  but  there  is  much 
difficulty  about  delatinisation.  Is  this  more  correct  than  Oronce 
Fine,  which  the  translator  of  De  Thou  uses  ?  Or  than  Horonce 
Phine,  which  older  writers  give  ?  I  cannot  understand  why  M. 
de  Viette  should  be  called  Viete,  because  his  Latin  name  is  Vieta. 
It  is  difficult  to  restore  Buteo  ;  for  not  only  now  is  butor  a  block- 
head as  well  as  a  bird,  but  we  really  cannot  know  what  kind  of 
bird  Buteo  stood  for.  We  may  be  sure  that  Madame  Fine  was 
Denise  Blanche  ;  for  Dionysia  Candida  can  mean  nothing  else. 
Let  her  shade  rejoice  in  the  fame  which  Hubertus  Sussannaeus 
has  given  her. 

I  ought  to  add  that  the  quadrature  of  Orontius,  and  solutions 
of  all  the  other  difficulties,  were  first  published  in  *  De  Kebus 
Mathematicis  Hactenus  Desideratis,'  of  which  I  have  not  the  date. 

Nicolai  Baymari  Ursi  Dithmarsi  Fundamentum  Astronomicum, 
id  est,  nova  doctrina  sinuum  et  triangulorum.  .  .  .  Strasburg, 
1588,  4to. 

People  choose  the  name  of  this  astronomer  for  themselves :  I 
take  Ursus,  because  he  was  a  bear.  This  book  gave  the  quadra- 
ture of  Simon  Duchesne,  or  a  Quercu,  which  excited  Peter  Metius, 
as  presently  noticed.  It  also  gave  that  unintelligible  reference  to 
Justus  Byrgius  which  has  been  used  in  the  discussion  about  the 
invention  of  logarithms. 

The  real  name  of  Duchesne  is  Van  der  Eycke.  I  have  met 
with  a  tract  in  Dutch,  Letterkundige  Aanteekeningen,  upon  Van 
Eycke,  Van  Ceulen,  &c.,  by  J.  J.  Dodt  van  Flensburg,  which  I 
make  out  to  be  since  1841  in  date.  I  should  much  like  a  trans- 

»  2 


36  A   BUDGET   OF  PARADOXES. 

lation  of  this  tract  to  be  printed,  say  in  the  Phil.  Mag.  Dutch 
would  be  clear  English  if  it  were  properly  spelt.  For  example, 
learn-master  would  be  seen  at  once  to  be  teacher ;  but  they  will 
spell  it  leermeester.  Of  these  they  write  as  van  deze;  widow 
they  make  weduwe.  All  this  is  plain  to  me,  who  never  saw  a 
Dutch  dictionary  in  my  life ;  but  many  of  their  mispellings  are 
quite  unconquerable. 

Jacobus  Falco  Valentinus,  miles  Ordinis  Montesiani,  hanc  circuli 
quadraturam  invenit.     Antwerp,  1589,  4to. 

The  attempt  is  more  than  commonly  worthless ;  but  as  Mon- 
tucla  and  others  have  referred  to  the  verses  at  the  end,  and  as  the 
tract  is  of  the  rarest,  I  will  quote  them  : — 

Circulus  loquitur. 

Vocabar  ante  circulus 
Eramque  curvus  undique 
Ut  alta  solis  orbita 
Et  arcus  ille  nubium. 
Eram  figura  nobilis 
Carensque  sola  origine 
Carensque  sola  termino. 
Modo  indecora  prodeo 
Novisque  foedor  angulis. 
Nee  hoc  peregit  Archytas 
Neque  Icari  pater  neque 
THUS  lapete  filius. 
Quis  ergo  casus  aut  Deus 
Meam  quadravit  aream  ? 

Hespondet  auctor. 

Ad  alta  Turiee  ostia 
Lacumque  limpidissimum 
Sita  est  beata  ci vitas 
Parum  Saguntus  abfuit 
Abestque  Sucro  plusculum. 
Hie  est  poeta  quispiam 
Libenter  astra  consulens 
Sibique  semper  arrogans 
Negata  doctioribus. 
Senex  ubique  cogitans 
Sui  frequenter  immemor 
Nee  explicare  circinum 


PETER   BUNGUS.  37 

Nee  exarare  lineas 
Sciens  ut  ipse  praedicat. 
Hie  ergo  bellus  artifex 
Tuam  quadra vit  aream. 

Falco's  verses  are  pretty,  if  the  w  ~  mysteries  be  correct ;  but  of 
these  things  I  have  forgotten — what  I  knew.  [One  mistake  has 
been  pointed  out  to  me  :  it  is  Archytas]. 

As  a  specimen  of  the  way  in  which  history  is  written,  I  copy 
the  account  which  Montucla — who  is  accurate  when  he  writes 
about  what  he  has  seen — gives  of  these  verses.  He  gives  the  date 
1587  ;  he  places  the  verses  at  the  beginning  instead  of  the  end; 
he  says  the  circle  thanks  its  quadrator  affectionately ;  and  he 
says  the  good  and  modest  chevalier  gives  all  the  glory  to  the 
patron  saint  of  his  order.  All  of  little  consequence,  as  it  happens ; 
but  writing  at  second-hand  makes  as  complete  mistakes  about 
more  important  matters. 

Petri  Biingi  Bergomatis  Numeronim  mysteria.      Bergomi  [Ber- 
gamo], 1591,  4to.     Second  Edition. 

The  first  edition  is  said  to  be  of  1585  ;  the  third,  Paris,  1618. 
Bungus  is  not  for  my  purpose  on  his  own  score,  but  those  who 
gave  the  numbers  their  mysterious  characters :  he  is  but  a  collector. 
He  quotes  or  uses  402  authors,  as  we  are  informed  by  his  list : 
this  just  beats  Warburton,  whom  some  eulogist  or  satirist,  I  forget 
which,  holds  up  as  having  used  400  authors  in  some  one  work. 
Bungus  goes  through  1,  2,  3,  &c.,  and  gives  the  account  of  every- 
thing remarkable  in  which  each  number  occurs ;  his  accounts  not 
being  always  mysterious.  The  numbers  which  have  nothing  to 
say  for  themselves  are  omitted :  thus  there  is  a  gap  between  50 
and  60.  In  treating  666,  Bungus,  a  good  Catholic,  could  not 
compliment  the  Pope  with  it,  but  he  fixes  it  on  Martin  Luther 
with  a  little  forcing.  If  from  A  to  I  represent  1-10,  from  K  to 
S  10-90,  and  from  T  to  Z  100-500,  we  see— 

MARTIN         LU      TERA 

30  1  80  100  9  40        20  200  100  5  80    1 

which  gives  666.     Again,  in  Hebrew,  Lulter  does  the  same : — 

i     n     h    1    *> 
200  400  30  6  30 

And  thus  two  can  play  at  any  game.  The  second  is  better 
than  the  first :  to  Latinise  the  surname  and  not  the  Christian 
name  is  very  unscholarlike.  The  last  number  mentioned  is  a 


38  A   BUDGET   OF   PARADOXES. 

thousand  millions ;  all  greater  numbers  are  dismissed  in  half  a 
page.  Then  follows  an  accurate  distinction  between  number 
and  multitude — a  thing  much  wanted  both  in  arithmetic  and 
logic. 

What  may  be  the  use  of  such  a  book  as  this  ?     The  last  occa- 
sion on  which  it  was  used  was  the  following.     Fifteen  or  sixteen 
years  ago  the  Koyal  Society  determined  to  restrict  the  number  of 
yearly  admissions  to  fifteen  men  of  science,  and  noblemen  ad 
libitum ;  the  men  of  science  being  selected  and  recommended  by 
the  Council,  with  a  power,  since  practically  surrendered,  to  the 
Society  to  elect  more.     This  plan  appears  to  me  to  be  directly 
against  the  spirit  of  their  charter,  the  true  intent  of  which  is, 
that  all  who  are  fit  should  be  allowed  to  promote  natural  know- 
ledge in  association,  from  and  after  the  time  at  which  they  are 
both  fit  and  willing.     It  is  also  working  more  absurdly  from  year 
to  year ;  the  tariff  of  fifteen  per  annum  will  soon  amoirnt  to  the 
practical  exclusion  of  many  who  would  be  very  useful.     This 
begins  to  be  felt  already,  I  suspect.     But,  as  appears  above,  the 
body  of  the  Society  has  the  remedy  in  its  own  hands.     When  the 
alteration  was  discussed  by  the  Council,  my  friend  the  late  Mr. 
Gralloway,  then  one  of   the  body,  opposed   it  strongly,  and  in- 
quired particularly  into  the  reason  why  fifteen,  of  all  numbers, 
was  the  one  to  be  selected.     Was  it  because  fifteen  is  seven  and 
eight,  typifying  the  Old  Testament  Sabbath,  and  the  New  Testa- 
ment day  of  the  resurrection  following  ?     Was  it  because  Paul 
strove  fifteen  days  against  Peter,  proving  that  he  was  a  doctor 
both  of  the  Old  and  New  Testament  ?     Was  it  because  the  prophet 
Hosea  bought  a  lady  for  fifteen  pieces  of  silver  ?     Was  it  because, 
according  to  Micah,  seven  shepherds   and   eight    chiefs  should 
waste  the  Assyrians?      Was  it  because  Ecclesiastes   commands 
equal  reverence  to  be  given  to  both  Testaments — such  was  the 
interpretation — in  the  words  '  Give  a  portion  to  seven,  and  also 
to  eight '  ?     Was  it  because  the  waters  of  the  Deluge  rose  fifteen 
cubits  above    the    mountains  ? — or  because   they   lasted   fifteen 
decades  of  days  ?     Was  it  because  Ezekiel's  temple  had  fifteen 
steps  ?     Was  it  because  Jacob's  ladder  has  been  supposed  to  have 
had  fifteen  steps  ?     Was  it  because  fifteen  years  were  added  to 
the  life  of  Hezekiah  ?     Was  it  because  the  feast  of  unleavened 
bread  was  on  the  fifteenth  day  of  the  month  ?     Was  it  because 
the  scene  of  the  Ascension  was  fifteen  stadia  from  Jerusalem  ? 
Was   it   because   the    stone-masons    and    porters    employed    in 
Solomon's  temple  amounted  to  fifteen  myriads  ?  &c.     The  Council 
were  amused  and  astounded  by  the  volley  of  fifteens  which  was 


THE   FIFTEENS   OF   BUNGUS.  39 

fired  at  them ;  they  knowing  nothing  about  Bungus,  of  which 
Mr.  Gralloway — who  did  not,  as  the  French  say,  indicate  his 
sources — possessed  the  copy  now  before  me.  In  giving  this 
anecdote  I  give  a  specimen  of  the  book,  which  is  exceedingly  rare. 
Should  another  edition  ever  appear,  which  is  not  very  probable, 
he  would  be  but  a  bungling  Bungus  who  should  forget  the  fifteen 
of  the  Royal  Society. 

[I  make  a  remark  on  the  different  colours  which  the  same 
person  gives  to  one  story,  according  to  the  bias  under  which  he 
tells  it.  My  friend  Galloway  told  me  how  he  had  quizzed  the 
Council  of  the  Royal  Society,  to  my  great  amusement.  When- 
ever I  am  struck  by  the  words  of  any  one,  I  carry  away  a  vivid 
recollection  of  position,  gestures,  tones,  &c.  I  do  not  know 
whether  this  be  common  or  uncommon.  I  never  recall  this  joke 
without  seeing  before  me  my  friend,  leaning  against  his  book- 
case, with  Bungus  open  in  his  hand,  and  a  certain  half-deprecia- 
tory tone  which  he  often  used  when  speaking  of  himself.  Long 
after  his  death,  an  F.E.S.  who  was  present  at  the  discussion,  told 
me  the  story.  I  did  not  say  I  had  heard  it,  but  I  watched  him, 
with  Gralloway  at  the  bookcase  before  me.  I  wanted  to  see 
whether  the  two  would  agree  as  to  the  fact  of  an  enormous 
budget  of  fifteens  having  been  fired  at  the  Council,  and  they 
did  agree  perfectly.  But  when  the  paragraph  of  the  Budget 
appeared  in  the  Athenaeum,  my  friend,  who  seemed  rather  to 
object  to  the  shewing-up,  assured  me  that  the  thing  was  grossly 
exaggerated  ;  there  was  indeed  a  fifteen  or  two,  but  nothing  like 
the  number  I  had  given.  I  had,  however,  taken  sharp  note  of 
the  previous  narration. 

I  will  give  another  instance.  An  Indian  officer  gave  me  an 
account  of  an  elephant,  as  follows.  A  detachment  was  on  the 
march,  and  one  of  the  gun-carriages  got  a  wheel  off  the  track, 
so  that  it  was  also  off  the  ground,  and  hanging  over  a  precipice. 
If  the  bullocks  had  moved  a  step,  carriages,  bullocks,  and  all 
must  have  been  precipitated.  No  one  knew  what  could  be  done 
until  some  one  proposed  to  bring  up  an  elephant,  and  let  him 
manage  it  his  own  way.  The  elephant  took  a  moment's  survey  of 
the  fix,  put  his  trunk  under  the  axle  of  the  free  wheel,  and  waited. 
The  surrounders,  who  saw  what  he  meant,  moved  the  bullocks 
gently  forward,  the  elephant  followed,  supporting  the  axle,  until 
there  was  ground  under  the  wheel,  when  he  let  it  quietly  down. 
From  all  I  had  heard  of  the  elephant,  this  was  not  too  much 
to  believe.  But  when,  years  afterwards,  I  reminded  my  friend 


40  A   BUDGET   OF  PARADOXES. 

of  his  story,  he  assured  me  that  I  had  misunderstood  him,  that 
the  elephant  was  directed  to  put  his  trunk  under  the  wheel,  and 
saw  in  a  moment  why.  This  is  reasonable  sagacity,  and  very 
likely  the  correct  account ;  but  I  am  quite  sure  that,  in  the  fit 
of  elephant-worship  under  which  the  story  was  first  told,  it  was 
told  as  I  have  first  stated  it.] 

[Jordani  Bruni  Nolani  de  Monade,  Numero  et  Figura  .  .  .  item  de 
Innumerabilibus,  Immense,  et  Infigurabili.  .  .  Frankfort,  1591, 
8vo. 

I  cannot  imagine  how  I  came  to  omit  a  writer  whom  I  have 
known  so  many  years,  unless  the  following  story  will  explain  it. 
The  officer  reproved  the  boatswain  for  perpetual  swearing ;  the 
boatswain  answered  that  he  heard  the  officers  swear.  '  Only  in 
an  emergency,'  said  the  officer.  'That's  just  it,'  replied  the 
other ;  '  a  boatswain's  life  is  a  life  of  'mergency.'  OKordano 
Bruno  was  all  paradox ;  and  my  mind  was  not  alive  to  his 
paradoxes,  just  as  my  ears  might  have  become  dead  to  the  boat- 
swain's oaths.  He  was,  as  has  been  said,  a  vorticist  before 
Descartes,  an  optimist  before  Leibnitz,  a  Copernican  before 
Gralileo.  It  would  be  easy  to  collect  a  hundred  strange  opinions 
of  his.  He  was  born  about  1550,  and  was  roasted  alive  at  Rome, 
February  17,  1600,  for  the  maintenance  and  defence  of  the  holy 
Church,  and  the  rights  and  liberties  of  the  same.  These  last 
words  are  from  the  writ  of  our  own  good  James  I.,  under  which 
Leggatt  was  roasted  at  Smithfield,  in  March  1612 ;  and  if  I  had  a 
.copy  of  the  instrument  under  which  Wightman  was  roasted  at 
Litchfield,  a  month  afterwards,  I  daresay  I  should  find  something 
quite  as  edifying.  1  extract  an  account  which  I  gave  of  Bruno 
in  the  Comp.  Aim.  for  1855  : — 

He  was  first  a  Dominican  priest,  then  a  Calvinist ;  and  was  roasted 
alive  "at  Rome,  in  1600,  for  as  many  heresies  of  opinion,  religious  and 
philosophical,  as  ever  lit  one  fire.  Some  defenders  of  the  papal  cause 
Lave  at  least  worded  their  accusations  so  to  be  understood  as  imputing 
to  him  villainous  actions.  But  it  is  positively  certain  that  his  death 
was  due  to  opinions  alone,  and  that  retractation,  even  after  sentence, 
would  have  saved  him.  There  exists  a  remarkable  letter,  written  from 
Home  on  the  very  clay  of  the  murder,  by  Scioppius  (the  celebrated 
scholar,  a  waspish  convert  from  Lutheranism,  known  by  his  hatred  to 
Protestants  and  Jesuits)  to  Rittershusius,  a  well-known  Lutheran 
writer  on  civil  and  cation  law,  whose  works  are  in  the  index  of  prohi- 
bited books.  This  letter  has  been  reprinted  by  Libri  (vol.  iv.  p.  407). 
The  writer  informs  his  friend  (whom  he  wished  to  convince  that  even  a 
Lutheran  would  have  burnt  Bruno)  that  all  Rome  would  tell  him  that 


GIOKDANO   BBUNO.  41 

Bruno  died  for  Lutheranism ;  but  this  is  because  the  Italians  do  not 
know  the  difference  between  one  heresy  and  another,  in  which  simpli- 
city (says  the  writei*)  may  God  preserve  them.  That  is  to  say,  they 
knew  the  difference  between  a  live  heretic  and  a  roasted  one  by  actual 
inspection,  but  had  no  idea  of  the  difference  between  a  Lutheran  and  a 
Calvinist.  The  countrymen  of  Boccaccio  would  have  smiled  at  the  idea 
which  the  German  scholar  entertained  of  them.  They  said  Bruno  was 
burnt  for  Lutheranism,  a  name  under  which  they  classed  all  Protestants : 
and  they  are  better  witnesses  than  Schopp,  or  Scioppius.  He  then 
proceeds  to  describe  to  big  Protestant  friend  (to  whom  he  would 
certainly  not  have  omitted  any  act  which  both  their  Churches  would 
have  condemned)  the  mass  of  opinions  with  which  Bruno  was  charged  ; 
as  that  there  are  innumerable  worlds,  that  souls  migrate,  that  Moses 
was  a  magician,  that  the  Scriptures  are  a  dream,  that  only  the  Hebrews 
descended  from  Adam  and  Eve,  that  the  devils  would  be  saved,  that 
Christ  was  a  magician  and  deservedly  put  to  death,  &c.  In  fact,  says 
he,  Bruno  has  advanced  all  that  was  ever  brought  forward  by  all 
heathen  philosophers,  and  by  all  heretics,  ancient  and  modern.  A  time 
for  retractation  was  given,  both  before  sentence  and  after,  which  should 
be  noted,  as  well  for  the  wretched  palliation  which  it  may  afford,  as  for 
the  additional  proof  it  gives  that  opinions,  and  opinions  only,  brought 
him  to  the  stake.  In  this  medley  of  charges  the  Scriptures  are  a  dream, 
while  Adam,  Eve,  devils,  and  salvation  are  truths,  and  the  Saviour  a 
deceiver.  We  have  examined  no  work  of  Bruno  except  the  De  Monade, 
8fc.,  mentioned  in  the  text.  A  strong  though  strange  theism  runs 
through  the  whole,  and  Moses,  Christ,  the  Fathers,  &c.,  are  cited  in  a 
manner  which  excites  no  remark  either  way.  Among  the  versions  of 
the  cause  of  Bruno's  death  is  atheism :  but  this  word  was  very  often 
used  to  denote  rejection  of  revelation,  not  merely  in  the  common  course 
of  dispute,  but  by  such  writers,  for  instance,  as  Brucker  and  Morhof. 
Thus  Morhof  says  of  the  De  Monade,  8fc.,  that  it  exhibits  no  manifest 
signs  of  atheism.  What  he  means  by  the  word  is  clear  enough,  when 
he  thus  speaks  of  a  work  which  acknowledges  God  in  hundreds  of 
places,  and  rejects  opinions  as  blasphemous  in  several.  The  work  of 
Bruno  in  which  his  astronomical  opinions  are  contained  is  De  Monade, 
8fc.  (Frankfort,  1591,  8vo).  He  is  the  most  thorough-going  Copernican 
possible,  and  throws  out  almost  every  opinion,  true  or  false,  which  has 
ever  been  discussed  by  astronomers,  from  the  theory  of  innumerable 
inhabited  worlds  and  systems  to  that  of  the  planetary  nature  of  comets. 
Libri  (vol.  iv.)  has  reprinted  the  most  striking  part  of  his  expressions 
of  Coperuican  opinion. 

The  Satanic  doctrine  that  a  Church  may  employ  force  in  aid 
of  its  dogma  is  supposed  to  be  obsolete  in  England,  except  as  an 
individual  paradox ;  but  this  is  difficult  to  settle.  Opinions 
are  much  divided  as  to  what  the  Roman  Church  would  do  in 


42  A  BUDGET   OE  PAKADOXES. 

England,  if  she  could :  any  one  who  doubts  that  she  claims  the 
right    does   not  deserve    an   answer.      When   the  hopes  of  the 
Tractarian  section  of  the  High  Church  were  in  bloom,  before  the 
most  conspicuous  intellects  among  them  had  transgressed  their 
ministry,  that  they  might  goto  their  own  place,  I  had  the  curiosity 
to  see  how  far  it  could  be  ascertained  whether  they  held  the 
only  doctrine  which  makes  me  the  personal  enemy  of  a  sect.     I 
found  in  one  of  their  tracts  the  assumption  of  a  right  to  per- 
secute,  modified  by  an  asserted  conviction  that  force  was  not 
efficient.      I   cannot  now   say   that   this  tract  was   one   of  the 
celebrated  ninety  ;  and  on  looking  at  the  collection  I  find  it  so 
poorly  furnished  with  contents,  &c.,  that  nothing  but  searching 
through  three  thick  volumes  would  decide.     In  these  volumes  I 
find,  augmenting  as  we  go  on,  declarations  about  the  character 
and  power  of  '  the  Church '  which  have  a  suspicious  appearance. 
The  suspicion  is   increased  by  that  curious  piece   of  sophistry, 
No.  87,  on  religious  reserve.     The  queer  paradoxes  of  that  tract 
leave  iis  in  doubt  as  to  everything  but  t^his,  that  the  church(man) 
is  not  bound  to  give  his  whole  counsel  in  all   things,  and  not 
bound  to  say  what  the  things  are  in  which  he  does  not  give  it. 
It  is  likely  enough  that  some   of  the  '  rights  and  liberties '  are 
but  scantily  described.     There  is  now  no  fear ;  but  the  time  was 
when,  if  not  fear,  there  might  be  a  looking  for  of  fear  to  come ; 
nobody  could  then  be  so  sure  as  we  now  are  that  the  lion  was 
only  asleep.     There  was  every  appearance  of  a  harder  fight  at 
hand  than  was  really  found  needful. 

Among  other  exquisite  quirks  of  interpretation  in  the  No.  87 
above  mentioned  is  the  following.  GTod  himself  employs  re- 
serve ;  he  is  said  to  be  decked  with  light  as  with  a  garment  (the 
old  or  prayer-book  version  of  Psalm  civ.  2).  To  an  ordinary 
apprehension  this  would  be  a  strong  image  of  display,  manifesta- 
tion, revelation ;  but  there  is  something  more.  '  Does  not  a 
garment  veil  in  some  measure  that  which  it  clothes  ?  Is  not 
that  very  light  concealment  ?  ' 

This  No.  87,  admitted  into  a  series,  fixes  upon  the  managers 
of  the  series,  who  permitted  its  introduction,  a  strong  presump- 
tion of  that  underhand  intent  with  which  they  were  charged. 
At  the  same  time  it  is  honourable  to  our  liberty  that  this  series 
could  be  published :  though  its  promoters  were  greatly  shocked 
when  the  Essayists  and  Bishop  Colenso  took  a  swing  on  the 
other  side.  When  No.  90  was  under  discussion,  Dr.  Maitland, 
the  librarian  at  Lambeth,  asked  Archbishop  Howley  a  question 
about  No.  89.  *  I  did  not  so  much  as  know  there  was  a  No.  89^ 


RITUALISM.  I-! 

was  the  answer.  I  am  almost  sure  I  have  seen  this  in  print, 
and  quite  sure  that  Dr.  Maitland  told  it  to  me.  It  is  creditable 
that  there  was  so  much  freedom ;  but  No.  90  was  too  bad,  and 
was  stopped. 

The  Tractarian  mania  has  now  (October  1866)  settled  down 
into  a  chronic  vestment  disease,  complicated  with  fits  of  tran- 
substantiation,  which  has  taken  the  name  of  Ritualism.  The 
common  sense  of  "our  national  character  will  not  put  up  with  a 
continuance  of  this  grotesque  folly  ;  millinery  in  all  its  branches 
will  at  last  be  advertised  only  over  the  proper  shops.  I  am  told 
that  the  Eitualists  give  short  and  practical  sermons ;  if  so,  they 
may  do  good  in  the  end.  The  English  Establishment  has  always 
contained  those  who  want  an  excitement ;  the  New  Testament, 
in  its  plain  meaning,  can  do  little  for  them.  Since  the  Ee  volu- 
tion, Jacobitism,  Wesleyanism,  Evangelicism,  Puseyism,  and 
Eitualism,  have  come  on  in  turn,  and  have  furnished  hot  water 
for  those  who  could  not  wash  without  it.  If  the  Eitualists  should 
succeed  in  substituting  short  and  practical  teaching  for  the 
high-spiced  lectures  of  the  doctrinalists,  they  will  be  remembered 
with  praise.  John  the  Baptist  would  perhaps  not  have  brought 
all  Jerusalem  out  into  the  wilderness  by  his  plain  and  good 
sermons  :  it  was  the  camel's  hair  and  the  locusts  which  got  him 
a  congregation,  and  which,  perhaps,  added  force  to  his  precepts. 
When  at  school  I  heard  a  dialogue,  between  an  usher  and  the 

man  who  cleaned  the  shoes,  about  Mr. ,  a  minister,  a  very 

corporate  body  with  due  area  of  waistcoat.  '  He  is  a  man  of 
great  erudition,'  said  the  first.  '  Ah,  yes,  sir,'  said  Joe ;  '  any- 
one can  see  that  who  looks  at  that  silk  waistcoat.'] 

[When  I  said  at  the  outset  that  I  had  only  taken  books 
from  my  own  store,  I  should  have  added  that  I  did  not  make  any 
search  for  information  given  as  part  of  a  work.  Had  I  looked 
through  all  my  books,  I  might  have  made  some  curious  additions. 
For  instance,  in  Schott's  Magia  Naturalis  (vol.  iii.  pp.  756-778) 
is  an  account  of  the  quadrature  of  Gephyrauder,  as  he  is  mis- 
printed in  Montucla.  He  was  Thomas  Gephyrander  Salicetus; 
and  he  published  two  editions,  in  1608  and  1609 :  I  never  even 
heard  of  a  copy  of  either.  His  work  is  of  the  extreme  of  absurdity  : 
he  makes  a  distinction  between  geometrical  and  arithmetical  frac- 
tions, and  evolves  theorems  from  it.  More  curious  than  his  quad- 
rature is  his  name  ;  what  are  we  to  make  of  it  ?  If  a  German,  he  is 
probably  a  German  form  of  Bridgeman,  and  Salicetus  refers  him  to 
Weiden.  But  Thomas  was  hardly  a  German  Christian  name  of  his 


44  A   BUDGET   OF  PAEADOXES. 

time  ;  of  526  German  philosophers,  physicians,  lawyers,  and  theolo- 
gians who  were  biographed  by  Melchior  Adam,  only  two  are  of  this 
name.  Of  these  one  is  Thomas  Erastus,  the  physician  whose  theolo- 
gical writings  against  the  Church  as  a  separate  power  have  given  the 
name  of  Erastians  to  those  who  follow  his  doctrine,  whether  they 
have  heard  of  him  or  not.  Erastus  is  little  known ;  accordingly, 
some  have  supposed  that  he  must  be  Erastus,  the  friend  of  St. 
Paul  and  Timothy  (Acts  xix.  22 ;  2  Tim.  iv.  20  ;  Kom.  xvi.  23), 
but  what  this  gentleman  did  to  earn  the  character  is  not  hinted 
at.  P^ew  words  would  have  done  :  Grains  (Eom.  xvi.  23)  has  an 
immortality  which  many  more  noted  men  have  missed,  given  by 
John  Bunyan,  out  of  seven  words  of  St.  Paul.  I  was  once  told 
that  the  Erastians  got  their  name  from  Blastus,  and  I  could  not 
solve  bl  =  er :  at  last  I  remembered  that  Blastus  was  a  chamber- 
lain as  well  as  Erastus  ;  hence  the  association  which  caused  the 
mistake.  The  real  heresiarch  was  a  physician  who  died  in  1583  ; 
his  heresy  was  promulgated  in  a  work,  published  immediately 
after  his  death  by  his  widow,  De  Excommunicatione  Ecclesiastica. 
He  denied  the  power  of  excommunication  on  the  principle  above 
stated ;  and  was  answered  by  Beza.  The  work  was  translated  by 
Dr.  R.  Lee  (Edinb.  1844,  8vo).  The  other  is  Thomas  Grynseus, 
a  theologian,  nephew  of  Simon,  who  first  printed  Euclid  in  Greek ; 
of  him  Adam  says  that  of  works  he  published  none,  of  learned 
sons  four.  If  Gephyrander  were  a  Frenchman,  his  name  is  not  so 
easily  guessed  at ;  but  he  must  have  been  of  La  Saussaye.  The 
account  given  by  Schott  is  taken  from  a  certain  Father  Philip 
Colbinus,  who  wrote  against  him. 

In  some  manuscripts  lately  given  to  the  Eoyal  Society, 
David  Gregory,  who  seems  to  have  seen  Gephyrander's  work,  calls 
him  Salicetus  Westphalus,  which  is  probably  on  the  title-page. 
But  the  only  Weiden  I  can  find  is  in  Bavaria.  Murhard  has  both 
editions  in  his  Catalogue,  but  had  plainly  never  seen  the  books  : 
he  gives  the  author  as  Thomas  Gep.  Hyandrus,  Salicettus  West- 
phalus.  Murhard  •  is  a  very  old  referee  of  mine ;  but  who  the 
non  nominandus  was  to  see  Montucla's  Gephyrauder  in  Murhard's 
Gep.  Hyandrus,  both  writers  being  usually  accurate  ?] 


NAPIEK— GILBERT— BAPTIST  A  PORTA.  45 


A  plain  discoverie  of  the  whole  Revelation  of  St.  John  .  .  . 
whereunto  are  annexed  certain  oracles  of  Sibylla  .  .  .  Set  Foorth 
by  John  Napeir  L.  of  Marchiston.  London,  1611,  4to. 

The  first  edition  was  Edinburgh,  1593,  4to.  Napier  always 
believed  that  his  great  mission  was  to  upset  the  Pope,  and  that 
logarithms,  and  such  things,  were  merely  episodes  and  relaxations. 
It  is  a  pity  that  so  many  books  have  been  written  about  this 
matter,  while  Napier,  as  good  as  any,  is  forgotten  and  unread. 
He  is  one  of  the  first  who  gave  us  the  six  thousand  years.  '  There 
is  a  sentence  of  the  house  of  Elias  reserved  in  all  ages,  bearing 
these  words :  The  world  shall  stand  six  thousand  years,  and  then 
it  shall  be  consumed  by  fire  :  two  thousand  yeares  voide  or  without 
lawe,  two  thousand  yeares  under  the  law,  and  two  thousand 
yeares  shall  be  the  daies  of  the  Messias.  .  .  .' 

I  give  Napier's  parting  salute  :  it  is  a  killing  dilemma  : — 

In  summar  conclusion,  if  thou  o  Borne  aledges  thyselfe  reformed,  and 
to  beleeue  true  Christianisme,  then  beleeue  Saint  John  the  Disciple, 
whome  Christ  loued,  publikely  here  in  this  Reuelation  proclaiming  thy 
wracke,  but  if  thou  remain  Ethnick  in  thy  priuate  thoghts,  beleeuing 
the  old  Oracles  of  the  Sibyls  reuerently  keeped  somtime  in  thy  Capitol : 
then  doth  here  this  Sibyll  proclame  also  thy  wracke.  Repent  therefore 
alwayes,  in  this  thy  latter  breath,  as  thou  louest  thine  Eternall  salvation. 
Amen. 

— Strange  that  Napier  should  not  have  seen  that  this  appeal  could 
not  succeed,  unless  the  prophecies  of  the  Apocalypse  were  no  true 
prophecies  at  all. 

De  Magnete  magneticisque  corporibus,  et  de  magno  magnete 
tellure.  By  William  Gilbert.  London,  1600,  folio.— There  is 
a  second  edition  ;  and  a  third,  according  to  Watt. 

Of  the  great  work  on  the  magnet  there  is  no  need  to  speak, 
though  it  was  a  paradox  in  its  day.  The  posthumous  work  of 
Gilbert,  'De  Mundo  nostro  sublunari  philosophia  nova'  (Ams- 
terdam, 1651,  4to)  is,  as  the  title  indicates,  confined  to  the 
physics  of  the  globe  and  its  atmosphere.  It  has  never  excited 
attention :  I  should  hope  it  would  be  examined  with  our  present 
lights. 

Elementorum  Curvilineorium  Libri  tres.    By  John  Baptista  Porta. 

Rome,  1610,  4to. 

This  is  a  ridiculous  attempt,  which  defies  description,  except 
that  it  is  all  about  lunules.  Porta  was  a  voluminous  writer. 


46  A  BUDGET   OF  PARADOXES. 

His  printer  announces  fourteen  works  printed,  and  four  to  come, 
besides  thirteen  plays  printed,  and  eleven  waiting.  His  name  is, 
and  will  be,  current  in  treatises  on  physics  for  more  reasons  than 
one. 

Trattato  della  quadratura  del  cerchio.     Di  Pietro  Antonio  Cataldi. 
Bologna,  1612,  folio. 

Eheticus,  Vieta,  and  Cataldi  are  the  three  untiring  computers 
of  Germany,  France,  and  Italy ;  Napier  in  Scotland,  and  Briggs  in 
England,  come  just  after  them.  This  work  claims  a  place  as 
beginning  with  the  quadrature  of  Pellegrino  Borello  of  Reggio, 
who  will  have  the  circle  to  be  exactly  3  diameters  and  -^^  of  a 
diameter.  Cataldi,  taking  Van  Ceulen's  approximation,  works 
hard  at  the  finding  of  integers  which  nearly  represent  the  ratio. 
He  had  not  then  the  continued  fraction,  a  mode  of  representation 
which  he  gave  the  next  year  in  his  work  on  the  square  root.  He 
\has  but  twenty  of  Van  Ceulen's  thirty  places,  which  he  takes  from 
Clavius :  and  anyone  might  be  puzzled  to  know  whence  the  Italians 
got  the  result ;  Van  Ceulen,  in  1612,  not  having  been  translated 
from  Dutch.  But  Clavius  names  his  comrade  Grruenberger,  and 
attributes  the  approximation  to  them  jointly  ;  *  Lud.  a  Collen  et 
Chr.  Grruenbergerus  invenerunt,'  which  he  had  no  right  to  do, 
unless,  to  his  private  knowledge,  Grruenberger  had  verified  Van 
Ceulen.  And  Grruenberger  only  handed  over  twenty  of  the  places. 
But  here  is  one  instance,  out  of  many,  of  the  polyglot  character 
of  the  Jesuit  body,  and  its  advantages  in  literature. 

Philippi  Lausbergii  Cyclometrise  Novsa  Libri  Duo.    Middleburg, 
1616,  4to. 

This  is  one  of  the  legitimate  quadratures,  on  which  I  shall 
here  only  remark  that  by  candlelight  it  is  quadrature  under 
difficulties,  for  all  the  diagrams  are  in  red  ink. 

Recherches  Curieuses  des  Mesures  du   Monde.     By  S.  C.  de  V. 
Paris,  1626,  8vo.  (pp.  48). 

It  is  written  by  some  Count  for  his  son  ;  and  if  all  the  French 
nobility  would  have  given  their  sons  the  same  kind  of  instruction 
about  rank,  the  old  French  aristocracy  would  have  been  as  pros- 
perous at  this  moment  as  the  English  peerage  and  squireage.  I 
sent  the  tract  to  Capt.  Speke,  shortly  after  his  arrival  in  England, 
thinking  he  might  like  to  see  the  old  names  of  the  Ethiopian  pro- 
vinces. But  I  first  made  a  copy  of  all  that  relates  to  Prester  John, 
himself  a  paradox.  The  tract  contains,  inter  alia,  an  account  of 


PRESTER  JOHN.  47 

the  four  empires ;  of  the  great  Turk,  the  great  Tartar,  the  great 
Sophy,  and  the  great  Prester  John.  This  word  great  (grand), 
which  was  long  used  in  the  phrase  '  the  great  Turk,'  is  a  generic 
adjunct  to  an  emperor.  Of  the  Tartars  it  is  said  that  '  c'est  vne 
nation  prophane  et  barbaresque,  sale  et  vilaine,  qui  mangent  la 
chair  demie  crue,  qui  boiuent  du  laict  de  jument,  et  qui  n'vsent 
de  nappes  et  seruiettes  que  pour  essuyer  leurs  bouches  et  leurs 
mains.'  Many  persons  have  heard  of  Prester  John,  and  have 
a  very  indistinct  idea  of  him.  I  give  all  that  is  said  about  him, 
since  the  recent  discussions  about  the  Nile  may  give  an  interest 
to  the  old  notions  of  geography. — 

Le  grand  Prestre  Jean  qui  est  le  quatriesme  en  rang,  est  Empereur 
d'Ethiopie,  et  des  Abyssins,  et  se  vante  d'estre  issu  de  la  race  de  Dauid, 
comme  estant  descendu  de  la  Boyne  de  Saba,  Boyne  d'Ethiopie,  laqu?lle 
estant  venue  en  Hierusalem  pour  voir  la  sagesse  de  Salomou,  enuiron 
1'an   du   monde  2952,  s'en  retourna  grosse  d'vn  fils  qu'ils  nomment 
Moylech,  duquel  ils  disent  estre  descendus  en  ligne  directe.     Et  ainsi 
il  se  glorifie  d'estre  le  plus  ancien  Monarque  de  la  terre,  disant  que  son 
Empire  a  dure  plus  de  trois  mil  ans,  ce  que  nul  autre  Empire  ne  pent 
dire.     Aussi  met-il  en  ses  tiltres  ce  qui  s'ensuit :  Nous,  N.  Souuerain 
en  mes  Royaumes,  vniquement  ayme  de  Dieu,  colomne  de  la  foy,  sorty 
de  la  race  de  luda,  &c.     Les  limites  de  cet  Empire  touchent  a  la  mer 
Ronge,    et   aux   montagnes    d'Azuma   vers   1'Orient,    et   du  coste  de 
1' Occident,  il  est  borne  du  fleuue  du  Nil,  qui  le  separe  de  la  Nubie,  vers 
le  Septentrion  il  a  1'^Egypte,  et  au  Midy  les  Royaumes  de  Congo,  et  de 
Mozambique,   sa  longueur  contenant  quarante  degre,   qui  font   mille 
vingt  cinq  lieues,  et  ce  depuis  Congo  on  Mozambique  qui  sont  au  Midy, 
iusqu'en  ^-Egypte  qui  est  au  Septentrion,  et  sa  largeur  contenant  depuis 
le  Nil  qui  est  a  1' Occident,  iusqu'aux  montagnes  d'Azuma,  qui  sont  a 
1'Orient,  sept  cens  vingt  cinq  lieues,  qui  font  vingt  neuf  degrez.     Get 
empire  a  sous  soy  trente  grandes  Prouinces,   scavoir,  Medra,  Gaga, 
Alchy,    Cedalon,    Mantro,    Finazam,    Barnaquez,     Ambiam,     Fungy, 
Angote,  Cigremaon,   Gorga  Cafatez,  Zastanla,  Zeth,  Barly,  Belangana, 
Tygra,    Gorgany,   Barganaza,   d'Ancut,   Dargaly  Ambiacatina,   Cara- 
cogly,    Amara    .     Maon  (sic),  Guegiera,  Bally,  Dobora   et  Macheda. 
Toutes  ces  Prouinces  cy  dessus  sont  situees  iustement  sous  la  ligne 
equinoxiale,  entres  les  Tropiques  de  Capricorne,  et  de  Cancer.     Mais 
elles  s'approchent  de  nostre   Tropiqne,  de  deux  cens  cinquante  lieues 
plus  qu' elles  ne  font  de  I'autre  Tropique.     Ce  mot  de  Prestre  Jean 
signifie  grand  Seigneur,  et  n'est  pas  Prestre  comme  plusieurs  pense,  il  a 
este  tousiours  Chrestien,  mais  souuent  Schismatique  :  maintenant  il  est 
Catholique,  et  reconnaist  le  Pape  pour  Sounerain  Pontife.     I'ay  veu 
quelqu'vn  des  ses  Euesques,  estant  en  Hierusalem,  auec  lequel  i'ay 
confere  souuent  par  le  moyen  de  nostre  trucheman :  il  estoit  d'vn  port 
graue  et  serieux,  succiur  (sic)  en  son  parler,  mais  subtil  a  merueilles 
en  tout  ce  qu'il  disoit.     II  prenoit   grand  plaisir  au  recit  (me  je  luy 


48  A  BUDGET   OF  PARADOXES. 

faisais  de  nos  belles  ceremonies,  et  de  la  granite  de  nos  Prelats  enleurs 
habits  Pontificaux,  et  autres  choses  que  je  laisse  pour  dire,  que  1'Ethi- 
opien  est  ioyoux  et  gaillard,  ne  ressemblant  en  rien  a  la  salete  du  Tar- 
tare,  ny  a  1'affreux  regard  du  miserable  Arabe,  mais  ils  sont  fins  et 
cauteleux,  et  ne  se  fient  en  personne,  soup9onneux  a  merueilles,  et  fort 
devotieux,  ils  ne  sont  du  tout  noirs  comme  1'on  croit,  i'entens  parler  de 
ceux  qui  ne  sont  pas  sous  la  ligne  Equinoxiale,  ny  trop  proches  d'icelle, 
car  ceux  qui  sont  dessous  sont  les  Mores  que  nous  voyons. 

It  will  be  observed  that  the  author  speaks  of  his  conversation 
with  an  Ethiopian  bishop,  about  that  bishop's  sovereign.  Some- 
thing must  have  passed  between  the  two  which  satisfied  the 
writer  that  the  bishop  acknowledged  his  own  sovereign  under 
some  title  answering  to  Prester  John. 

De  Cometa  anni  1618  dissertationes  Thomae  Fieni  et  Liberti 
Fromondi.  .  .  Equidem  Thomee  Fieni  epistolica  queBstio,  An 
verum  sit  Coelum  moveri  et  Terram  quiescere  ?  London,  1670, 
8vo. 

This  tract  of  Fienus  against  the  motion  of  the  earth  is  a  reprint 
of  one  published  in  1619.  I  have  given  an  account  of  it  as  a 
good  summary  of  arguments  of  the  time,  in  the  Companion  to  the 
Almanac  for  1836. 

Willebrordi  Snellii.     R.  F.  Cyclometricus.     Leyden,  1621,  4to. 

This  is  a  celebrated  work  on  the  approximative  quadrature, 
which,  having  the  suspicious  word  oyclometricus,  must  be  noticed 
here  for  distinction. 

1620.  In  this  year,  Francis  Bacon  published  his  'Novum 
Organum,'  which  was  long  held  in  England — but  not  until  the 
last  century — to  be  the  work  which  taught  Newton  and  all  his 
successors  how  to  philosophise.  That  Newton  never  mentions 
Bacon,  nor  alludes  in  any  way  to  his  works,  passed  for  nothing. 
Here  and  there  a  parodoxer  ventured  not  to  find  all  this  teaching 
in  Bacon,  but  he  was  pronounced  blind.  In  our  day  it  begins 
to  be  seen  that,  great  as  Bacon  was,  and  great  as  his  book  really 
is,  he  is  not  the  philosophical  father  of  modern  discovery. 

But  old  prepossession  will  find  reason  for  anything.  A  learned 
friend  of  mine  wrote  to  me  that  he  had  discovered  proof  that 
Newton  owned  Bacon  for  his  master :  the  proof  was  that  Newton, 
in  some  of  his  earlier  writings,  used  the  phrase  experimentum 
crucis,  which  is  Bacon's.  Newton  may  have  read  some  of  Bacon, 
though  no  proof  of  it  appears.  I  have  a  dim  idea  that  I  once 
saw  the  two  words  attributed  to  the  alchemists :  if  so,  there  is 


FRANCIS   BACON.  49 

another  explanation ;  for  Newton   was   deeply  read   in   the   al- 
chemists. 

I  subjoin  a  review  which  I  wrote  of  the  splendid  edition  of 
Bacon  by  Spedding,  Ellis,  and  Heath.  All  the  opinions  therein 
expressed  had  been  formed  by  me  long  before :  most  of  the 
materials  were  collected  for  another  purpose. 

The   Works   of  Francis    Bacon.      Edited   by    James    Spedding, 
R.  Leslie  Ellis,  and  Douglas  D.  Heath.     5  vols. 

No  knowledge  of  nature  without  experiment  and  observation  : 
so  said  Aristotle,  so  said  Bacon,  so  acted  Copernicus,  Tycho  Brahe, 
Gilbert,  Kepler,  Galileo,  Harvey,  &c.,  before  Bacon  wrote.  No 
derived  knowledge  until  experiment  and  observation  are  con- 
cluded :  so  said  Bacon,  and  no  one  else.  We  do  not  mean  to  say 
that  he  laid  down  his  principle  in  these  words,  or  that  he  carried 
it  to  the  utmost  extreme :  we  mean  that  Bacon's  ruling  idea  was 
the  collection  of  enormous  masses  of  facts,  and  then  digested 
processes  of  arrangement  and  elimination,  so  artistically  contrived, 
that  a  man  of  common  intelligence,  without  any  unusual  sagacity, 
should  be  able  to  announce  the  truth  sought  for.  Let  Bacon 
speak  for  himself,  in  his  editor's  English  : — 

But  the  course  I  propose  for  the  discovery  of  sciences  is  such  as 
leaves  but  little  to  the  acuteness  and  strength  of  wits,  but  places  all  wits 
and  understandings  nearly  on  a  level.  For,  as  in  the  drawing  of  a  straight 
line  or  a  perfect  circle,  much  depends  on  the  steadiness  and  practice  of 
the  hand,  if  it  be  done  by  aim  of  hand  only,  but  if  with  the  aid  of  rule 
or  compass  little  or  nothing,  so  it  is  exactly  with  my  plan.  .  .  For 
my  way  of  discovering  sciences  goes  far  to  level  men's  wits,  and  leaves 
but  little  to  individual  excellence ;  because  it  performs  everything  by 
the  surest  rules  and  demonstrations. 

To  show  that  we  do  not  strain  Bacon's  meaning,  we  add  what 
is  said  by  Hooke,  whom  we  have  already  mentioned  as  his  pro- 
fessed disciple,  and,  we  believe,  his  only  disciple  of  the  day  of 
Newton.  We  must,  however,  remind  the  reader  that  Hooke  was 
very  little  of  a  mathematician,  and  spoke  of  algebra  from  his  own 
idea  of  what  others  had  tol'd  him  : — 

The  intellect  is  not  to  be  suffered  to  act  without  its  helps,  but  is 
continually  to  be  assisted  by  some  method  or  engine,  which  shall 
be  as  a  guide  to  regulate  its  actions,  so  as  that  it  shall  not  be  able  to 
act  amiss.  Of  this  engine,  no  man  except  the  incomparable  Verulam 
hath  had  any  thoughts,  and  he  indeed  hath  promoted  it  to  a  very  good 
pitch  ;  but  there  is  yet  somewhat  more  to  be  added,  which  lie  seemed 
to  want  time  to  complete.  By  this,  as  by  that  art  of  algebra  in  geo- 

£ 


50  A  BUDGET   OF  PARADOXES. 

metry,  'twill  be  very  easy  to  proceed  in  any  natural  inquiry,  regularly 
and  certainly.  .  .  For  as  'tis  very  hard  for  the  most  acute  wit  to  find 
out  any  difficult  problem  in  geometry  without  the  help  of  algebra  .  .  . 
and  altogether  as  easy  for  the  meanest  capacity  acting  by  that  method 
to  complete  and  perfect  it,  so  will  it  be  in  the  inquiry  after  natural 
.  knowledge. 

Bacon  did  not  live  to  mature  the  whole  of  this  plan.  Are  we 
really  to  believe  that  if  he  had  completed  the  '  Instauratio '  we 
who  write  this — and  who  feel  ourselves  growing  bigger  as  we 
write  it — should  have  been  on  a  level  with  Newton  in  physical 
discovery?  Bacon  asks  this  belief  of  us,  and  does  not  get  it. 
But  it  may  be  said,  Your  business  is  with  what  he  did  leave, 
and  with  its  consequences.  Be  it  so.  Mr.  Ellis  says  :  l  That  his 
method  is  impracticable  cannot,  I  think,  be  denied,  if  we  reflect 
not  only  that  it  never  has  produced  any  result,  but  also  that  the 
process  by  which  scientific  truths  have  been  established  cannot 
be  so  presented  as  even  to  appear  to  be  in  accordance  with  it.' 
That  this  is  very  true  is  well  known  to  all  who  have  studied  the 
history  of  discovery :  those  who  deny  it  are  bound  to  establish 
either  that  some  great  discovery  has  been  made  by  Bacon's 
method — we  mean  by  the  part  peculiar -to  Bacon — or,  better  still, 
to  show  that  some  new  discovery  can  be  made,  by  actually  making- 
it.  No  general  talk  about  induction :  no  reliance  upon  the 
mere  fact  that  certain  experiments  or  observations  have  been 
made  ;  let  us  see  where  Bacon's  induction  has  been  actually 
used  or  can  be  used.  Mere  induction,  enumeratio  simplex,  is 
spoken  of  by  himself  with  contempt,  as  utterly  incompetent. 
For  Bacon  knew  well  that  a  thousand  instances  may  be  contra- 
dicted by  the  thousand  and  first :  so  that  no  enumeration  of 
instances,  however  large,  is  '  sure  demonstration,'  so  long  as  any 
are  left. 

The  immortal  Harvey,  who  was  inventing — we  use  the  word 
in  its  old  sense — the  circulation  of  the  blood,  while  Bacon  was  in 
,  the  full  flow  of  thought  upon  his  system,  may  be  trusted  to  say 
whether,  when  the  system  appeared,  he  found  any  likeness  in  it 
to  his  own  processes,  or  what  would  have  been  any  help  to  him, 
if  he  had  waited  for  the  '  Novum  Organum.'  He  said  of  Bacon, 
*  He  writes  philosophy  like  a  Lord  Chancellor.'  This  has  been 
generally  supposed  to  be  only  a  sneer  at  the  sutor  ultra  crepidam ; 
but  we  cannot  help  suspecting  that  there  was  more  intended  by 
it.  To  us,  Bacon  is  eminently  the  philosopher  of  error  prevented, 
not  of  progress  facilitated.  When  we  throw  off  the  idea  of  being 
led  right,  and  betake  ourselves  to  that  of  being  kept  from  going 


FRANCIS   BACON.  51 

wrong,  we  read  his  writings  with  a  sense  of  their  usefulness,  his 
genius,  and  their  probable  effect  upon  purely  experimental  science, 
which  we  can  be  conscious  of  upon  no  other  supposition.  It 
amuses  us  to  have  to  add  that  the  part  of  Aristotle's  logic  of 
which  he  saw  the  value  was  the  book  on  refutation  of  fallacies. 
Now  is  this  not  the  notion  of  things  to  which  the  bias  of  a 
practised  lawyer  might  lead  him  ?  In  the  case  which  is  before 
the  Court,  generally  speaking,  truth  lurks  somewhere  about  the 
facts,  and  the  elimination  of  all  error  will  show  it  in  the  residuum. 
The  two  senses  of  the  word  law  come  in  so  as  to  look  almost  like 
a  play  upon  words.  The  judge  can  apply  the  law  so  soon  as  the 
facts  are  settled  :  the  physical  philosopher  has  to  deduce  the  law 
from  the  facts.  Wait,  says  the  judge,  until  the  facts  are  deter- 
mined :  did  the  prisoner  take  the  goods  with  felonious  intent  ? 
did  the  defendant  give  what  amounts  to  a  warranty  ?  or  the  like. 
Wait,  says  Bacon,  until  all  the  facts,  or  all  the  obtainable  facts, 
are  brought  in  :  apply  my  rules  of  separation  to  the  facts,  and  the 
result  shall  come  out  as  easily  as  by  ruler  and  compasses.  We  think 
it  possible  that  Harvey  might  allude  to  the  legal  character  of 
Bacon's  notions :  we  can  hardly  conceive  so  acute  a  man,  after 
seeing  what  manner  of  writer  Bacon  was,  meaning  only  that  he 
was  a  lawyer  and  had  better  stick  to  his  business.  We  do  our- 
selves believe  that  Bacon's  philosophy  more  resembles  the  action 
of  mind  of  a  common-law  judge — not  a  Chancellor — than  that  of 
the  physical  inquirers  who  have  been  supposed  to  follow  in  his 
steps.  It  seems  to  us  that  Bacon's  argument  is,  there  can  be 
nothing  of  law  but  what  must  be  either  perceptible,  or  mechani- 
cally deducible,  when  all  the  results  of  law,  as  exhibited  in 
phenomena,  are  before  us.  Now  the  truth  is,  that  the  physical 
philosopher  has  frequently  to  conceive  law  which  never  was  in  his 
previous  thought — to  educe  the  unknown,  not  to  choose  among 
the  known.  Physical  discovery  would  be  very  easy  work  if  the 
inquirer  could  lay  down  his  this,  his  that,  and  his  t'other,  and  say, 
'  Now,  one  of  these  it  must  be ;  let  us  proceed  to  try  which.' 
Often  has  he  done  this,  and  failed ;  often  has  the  truth  turned 
out  to  be  neither  this,  that,  nor  t'other.  Bacon  seems  to  us  to 
think  that  the  philosopher  is  a  judge  who  has  to  choose,  upon 
ascertained  facts,  which  of  known  statutes  is  to  rule  the  decision : 
he  appears  to  us  more  like  a  person  who  is  to  write  the  statute- 
book,  with  no  guide  except  cases  and  decisions  presented  in  all 
their  confusion  and  all  their  conflict. 

Let    us    take   the    well-known  first  aphorism  of  the  '  Novum 
Organum  : ' 

B   2 


52  A  BUDGET  OF  PAEA  BOXES. 

Man  being  the  servant  and  interpreter  of  nature,  can  do  and  under- 
stand so  much,  and  so  much  only,  as  he  has  observed  in  fact  or  in 
thought  of  the  course  of  nature  :  beyond  this  he  neither  knows  anything 
nor  can  do  anything. 

This  aphorism  is  placed  by  Sir  John  Herschel  at  the  head  of 
his  '  Discourse  on  the  Study  of  Natural  Philosophy  : '  a  book  con- 
taining notions  of  discovery  far  beyond  any  of  which  Bacon  ever 
dreamed ;  and  this  because  it  was  written  after  discovery,  instead 
of  before.  Sir  John  Herschel,  in  his  version,  has  avoided  the 
translation  of  re  vel  mente  observaverit,  and  gives  us  only  '  by  his 
observation  of  the  order  of  nature.'  In  making  this  the  opening 
of  an  excellent  sermon,  he  has  imitated  the  theologians,  who 
often  employ  the  whole  time  of  the  discourse  in  stuffing  matter 
into  the  text,  instead  of  drawing  matter  out  of  it.  By  observation 
he  (Herschel)  means  the  whole  course  of  discovery,  observation, 
hypothesis,  deduction,  comparison,  &c.  The  type  of  the  Baconian 
philosopher,  as  it  stood  in  his  mind,  had  been  derived  from  a 
noble  example,  his  own  father,  William  Herschel,  an  inquirer 
whose  processes  would  have  been  held  by  Bacon  to  have  been 
vague,  insufficient,  compounded  of  chance  work  and  sagacity,  and 
too  meagre  of  facts  to  deserve  the  name  of  induction.  In  another 
work,  his  treatise  on  Astronomy,  Sir  John  Herschel,  after  noting 
that  a  popular  account  can  only  place  the  reader  on  the  threshold, 
proceeds  to  speak  as  follows  of  all  the  higher  departments  of 
science.  The  italics  are  his  own  : — 

Admission  to  its  sanctuary,  and  to  the  privileges  and  feelings  of 
a  votary,  is  only  to  be  gained  by  one  means — sound  and  sufficient 
knowledge  of  mathematics,  tJte  great  instrument  of  all  exact  inquiry, 
without  which  no  man  can  ever  make  such  advances  in  this  or  any  other 
of  the  higher  departments  of  science  as  can  entitle  him.  to  form  an  inde- 
pendent opinion  on  any  subject  of  discussion  within  their  range. 

How  is  this?  Man  can  know  no  more  than  he  gets  from 
observation,  and  yet  mathematics  is  the  great  instrument  of  all 
exact  inquiry.  Are  the  results  of  mathematical  deduction  results 
of  observation  ?  We  think  it  likely  that  Sir  John  Herschel 
would  reply  that  Bacon,  in  coupling  together  observare  re  and 
observare  mente,  has  done  what  some  wags  said  Newton  afterwards 
did  in  his  study-door — cut  a  large  hole  of  exit  for  the  large  cat, 
and  a  little  hole  for  the  little  cat.  But  Bacon  did  no  such  thing : 
he  never  included  any  deduction  under  observation.  To  mathe- 
matics he  had  a  dislike.  He  averred  that  logic  and  mathematics 
should  be  the  handmaids,  not  the  mistresses,  of  philosophy.  He 
ineant  that  they  should  play  a  subordinate  and  subsequent  part 


FRANCIS   BACON.  53 

in  the  dressing  of  the  vast  mass  of  facts  by  which  discovery  was 
to  be  rendered  equally  accessible  to  Newton  and  to  us.  Bacon 
himself  was  very  ignorant  of  all  that  had  been  done  by  mathe- 
matics ;  and,  strange  to  say,  he  especially  objected  to  astronomy 
being  handed  over  to  the  mathematicians.  Leverrier  and  Adams, 
calculating  an  unknown  planet  into  visible  existence  by  .enormous 
heaps  of  algebra,  furnish  the  last  comment  of  note  on  this 
specimen  of  the  goodness  of  Bacon's  views.  The  following 
account  of  his  knowledge  of  what  had  been  done  in  his  own  day 
or  before  it,  is  Mr.  Spedding's  collection  of  casual  remarks  in 
Mr.  Ellis's  several  prefaces  : — 

Though  he  paid  great  attention  to  astronomy,  discussed  carefully  the 
methods  in  which  it  ought  to  be  studied,  constructed  for  the  sati? fac- 
tion of  his  own  mind  an  elaborate  theory  of  the  heavens,  and  listened 
eagerly  for  the  news  from  the  stars  brought  by  Galileo's  telescope,  he 
appears  to  have  been  utterly  ignorant  of  the  discoveries  which  had 
just  been  made  by  Kepler's  calculations.     Though,  he  complained  in 
1623  of  the  want  of  compendious  methods  for  facilitating  arithmetical 
computations,  especially  with  regard  to  the  doctrine  of  Series,  and 
fully  recognized  the  importance  of  them  as  an  aid  to  physical  inquiries — 
he   does  not  say  a  word  about  Napier's  Logarithms,  which  had  been 
published  only  nine  years  before  and  reprinted  more  than  once  in  the 
interval.     He  complained  that  no  considerable  advance  had  been  made 
in  geometry  beyond  Euclid,  without  taking  any  notice  of  what  Lad 
been    done  by  Archimedes  and  Apollonius.     He  saw  the  importance  of 
determining  accurately  the  specific  gravities  of  different  substances,  and 
himself  attempted  to  form  a  table  of  them  by  a  rude  process  of  his  own, 
without  knowing  of  the  more  scientific  though  still  imperfect  methods 
previously  employed  by  Archimedes,  Ghetaldus,  and  Porta.     He  speaks 
of  the  tvpijxa  of  Archimedes  in  a  manner  which  implies  that  he  did  not 
clearly  apprehend  either  the  nature  of  the  problem  to  be  solved  or  the 
principles  upon  which  the  solution  depended.     In  reviewing  the  pro- 
gress of  mechanics,  he  makes  no  mention  of  Archimedes  himself,  or  of 
Stevinus,  Galileo.  Guldinus,  or  Ghetaldus.     He  makes  no  allusion  to 
the  theory  of  equilibrium.   He  observes  that  a  ball  of  one  pound  weight 
will  fall  nearly  as  fast  through  the  air  as  a  ball  of  two,  without  alluding 
to  the  theory  of  the  acceleration  of  falling  bodies,  which  had  been 
made  known  by  Galileo  more  than  thirty  years  before.     He  proposes  an 
inquiry  with  regard  to  the  lever — namely,  whether  in  a  balance  with 
arms  of  different  length  but  equal  weight  the  distance  from  the  fulcrum 
has  any  effect  upon  the  inclination, — though  the  theory  of  the  lever  was 
as  well  understood  in  his  own  time  as  it  is  now.     In  making  an  experi- 
ment of  his  own  to  ascertain  the  cause  of  the  motion  of  a  windmill,  he 
overlooks  an  obvious  circumstance  which  makes  the  experiment  incon- 
clusive, and  an  equally  obvious  variation  of  the  same  experiment  which 
would  Lave  sLown  Lim  that  Lis  tLeory  was  false.     He  speaks  of  the 


54  A  BUDGET   OF  PARADOXES. 

poles  of  the  earth  as  fixed,  in  a  manner  which  seems  to  imply  that  he 
was  not  acquainted  with  the  precession  of  the  equinoxes  ;  and  in 
another  place,  of  the  north  pole  being  above  and  the  south  pole  below, 
as  a  reason  why  in  our  hemisphere  the  north  winds  predominate  over 
the  south. 

Much  of  this  was  known  before,  but  such  a  summary  of  Bacon's 
want  of  knowledge  of  the  science  of  his  own  time  was  never  yet 
collected  in  one  place.  We  may  add,  that  Bacon  seems  to  have 
been  as  ignorant  of  Wright's  memorable  addition  to  the  resources 
of  navigation  as  of  Napier's  addition  to  the  means  of  calculation. 
Mathematics  was  beginning  to  be  the  great  instrument  of  exact 
inquiry :  Bacon  threw  the  science  aside,  from  ignorance,  just  at 
the  time  when  his  enormous  sagacity,  applied  to  knowledge, 
would  have  made  him  see  the  part  it  was  to  play.  If  Newton 
had  taken  Bacon  for  his  master,  not  he,  but  somebody  else,  would 
have  been  Newton. 

There  is  an  attempt  at  induction  going  on,  which  has  yielded 
little  or  no  fruit,  the  observations  made  in  the  meteorological 
observatories.  This  attempt  is  carried  on  in  a  manner  which 
would  have  caused  Bacon  to  dance  for  joy  ;  for  he  lived  in  times 
when  Chancellors  did  dance.  Eussia,  says  M.  Biot,  is  covered  by 
an  army  of  meteorographs,  with  generals,  high  officers,  subalterns, 
and  privates  with  fixed  and  defined  duties  of  observation.  Other 
countries  have  also  their  systematic  observations.  And  what  has 
come  of  it  ?  Nothing,  says  M.  Biot,  and  nothing  will  ever  come 
of  it :  the  veteran  mathematician  and  experimental  philosopher 
declares,  as  does  Mr.  Ellis,  that  no  single  branch  of  science  has 
ever  been  fruitfully  explored  in  this  way.  There  is  no  special 
object,  he  says.  Any  one  would  suppose  that  M.  Biot's  opinion, 
given  to  the  French  Government  upon  the  proposal  to  construct 
meteorological  observatories  in  Algeria  (Comptes  Rendue,vol.  xli, 
Dec.  31,  1855),  was  written  to  support  the  mythical  Bacon,  modern 
physics,  against  the  real  Bacon  of  the  '  Novum  Organum.'  There 
is  no  special  object.  In  these  words  lies  the  difference  between 
the  two  methods. 

[In  the  report  to  the  Greenwich  Board  of  Visitors  for  1867, 
Mr.  Airy,  speaking  of  the  increase  of  meteorological  observatories, 
remarks  '  Whether  the  effect  of  this  movement  will  be  that 
millions  of  useless  observations  will  be  added  to  the  millions  that 
already  exist,  or  whether  something  may  be  expected  to  result 
which  will  lead  to  a  meteorological  theory,  I  cannot  hazard  a 
conjecture.'  This  is  a  conjecture,  and  a  very  obvious  one :  if 


i'RANCIS   BACON.  55 

Mr.  Airy  would  have  given  2f  cZ.  for  the  chance  of  a  meteorological 
theory  formed  by  masses  of  observations,  he  would  never  have 
said  what  I  have  quoted.] 

Modern  discoveries  have  not  been  made  by  large  collections  of 
facts,  with  subsequent  discussion,  separation,  and  resulting  de- 
duction of  a  truth  thus  rendered  perceptible.  A  few  facts  have 
suggested  an  hypothesis,  which  means  a  supposition,  proper  to 
explain  them.  The  necessary  results  of  this  supposition  are 
worked  out,  and  then,  and  not  till  then,  other  facts  are  examined 
to  see  if  these  ulterior  results  are  found  in  nature.  The  trial  of 
the  hypothesis  is  the  special  object:  prior  to  which,  hypothesis 
must  have  been  started,  not  by  rule,  but  by  that  sagacity  of 
which  no  description  can  be  given,  precisely  because  the  very 
owners  of  it  do  not  act  under  laws  perceptible  to  themselves. 
The  inventor  of  hypothesis,  if  pressed  to  explain  his  method,  must 
answer  as  did  Zerah  Colburn,  when  asked  for  his  mode  of  instan- 
taneous calculation.  When  the  poor  boy  had  been  bothered  for 
some  time  in  this  manner,  he  cried  out  in  a  huff,  '  God  put  it 
into  my  head,  and  I  can't  put  it  into  yours.'  Wrong  hypotheses, 
rightly  worked  from,  have  produced  more  useful  results  than 
unguided  observation.  But  this  is  not  the  Baconian  plan. 
Charles  the  Second,  when  informed  of  the  state  of  navigation, 
founded  a  Baconian  observatory  at  Greenwich,  to  observe,  observe, 
observe  away  at  the  moon,  until  her  motions  were  known  suf- 
ficiently well  to  render  her  useful  in  guiding  the  seaman.  And 
no  doubt  Flamsteed's  observations,  twenty  or  thirty  of  them 
at  least,  were  of  signal  use.  But  how?  A  somewhat  fanciful 
thinker,  one  Kepler,  had  hit  upon  the  approximate  orbits  of  the 
planets  by  trying  one  hypothesis  after  another :  he  found  the 
ellipse,  which  the  Platonists,  well  despised  of  Bacon,  and  who 
would  have  despised  him  as  heartily  if  they  had  known  him,  had 
investigated  and  put  ready  to  hand  nearly  2,000  years  before. 
The  sun  in  the  focus,  the  motions  of  the  planet  more  and  more 
rapid  as  they  approach  the  sun,  led  Kepler — and  Bacon  would 
have  reproved  him  for  his  rashness — to  imagine  that  a  force  re- 
siding in  the  sun  might  move  the  planets,  a  force  inversely  as  the 
distance.  Bouillaud,  upon  a  fanciful  analogy,  rejected  the  inverse 
distance,  and,  rejecting  the  force  altogether,  declared  that  if  such 
a  thing  there  were,  it  would  be  as  the  inverse  square  of  the 
distance.  Newton,  ready  prepared  with  the  mathematics  of  the 
subject,  tried  the  fall  of  the  moon  towards  the  earth,  away  from 
her  tangent,  and  found  that,  as  compared  with  the  fall  of  a  stone, 


56  A  BUDGET   OF  PARADOXES. 

the  law  of  the  inverse  square  did  hold  for  the  moon.  He  deduced 
the  ellipse,  he  proceeded  to  deduce  the  effect  of  the  disturbance 
of  the  sun  upon  the  moon,  upon  the  assumed  theory  of  universal 
gravitation.  He  found  result  after  result  of  his  theory  in  con- 
formity with  observed  fact :  and,  by  aid  of  Flamsteed's  obser- 
vations, which  amended  what  mathematicians  call  his  constants, 
he  constructed  his  lunar  theory.  Had  it  not  been  for  Newton, 
the  whole  dynasty  of  Greenwich  astronomers,  from  Flamsteed  of 
happy  memory,  to  Airy  whom  Heaven  preserve,  might  have 
worked  away  at  nightly  observation  and  daily  reduction,  without 
any  remarkable  result :  looking  forward,  as  to  a  millennium,  to 
the  time  when  any  man  of  moderate  intelligence  was  to  see 
the  whole  explanation.  What  are  large  collections  of  facts  for  ? 
To  make  theories  from.,  says  Bacon :  to  try  ready-made  theories 
by,  says  the  history  of  discovery  :  it's  all  the  same,  says  the 
idolater  :  nonsense,  say  we  ! 

Time  and  space  run  short :  how  odd  it  is  that  of  the  three 
leading  ideas  of  mechanics,  time,  space,  and  matter,  the  first  two 
should  always  fail  a  reviewer  before  the  third.  We  might  dwell 
upon  many  points,  especially  if  we  attempted  a  more  descriptive 
account  of  the  valuable  edition  before  us.  No  one  need  imagine 
that  the  editors,  by  their  uncompromising  attack  upon  the  notion 
of  Bacon's  influence  common  even  among  mathematicians  and 
experimental  philosophers,  have  lowered  the  glory  of  the  great 
man  whom  it  was,  many  will  think,  their  business  to  defend 
through  thick  and  thin.  They  have  given  a  clearer  notion  of  his 
excellencies,  and  a  better  idea  of  the  power  of  his  mind,  than  ever 
we  saw  given  before.  Such  a  correction  as  theirs  must  have  come, 
and  soon,  for  as  Hallam  says — after  noting  that  the  'Novum 
Organum'  was  never  published  separately  in  England,  Bacon  has 
probably  been  more  read  in  the  last  thirty  years — now  forty — than 
in  the  two  hundred  years  which  preceded.  He  will  now  be  more 
read  than  ever  he  was.  The  history  of  the  intellectual  world  is 
the  history  of  the  worship  of  one  idol  after  another.  No  sooner 
is  it  clear  that  a  Hercules  has  appeared  among  men,  than  all 
that  imagination  can  conceive  of  strength  is  attributed  to  him, 
and  his  labours  are  recorded  in  the  heavens.  The  time  arrives 
when,  as  in  the  case  of  Aristotle,  a  new  deity  is  found,  and  the 
old  one  is  consigned  to  shame  and  reproach.  A  reaction  may 
afterwards  take  place,  and  this  is  now  happening  in  the  case  of 
the  Greek  philosopher.  The  end  of  the  process  is,  that  the  oppo- 
sing deities  take  their  places,  side  by  side,  in  a  Pantheon  dedicated 
pot  to  gods,  but  to  heroes. 


COPERNICUS  AND   THE  POPE.  57 

Passing  over  the  success  of  Bacon's  own  endeavours  to  improve 
the  details  of  physical  science,  which  was  next  to  nothing,  and  of 
his  method  as  a  whole,  which  has  never  been  practised,  we  might 
say  much  of  the  good  influence  of  his  writings.  Sound  wisdom, 
set  in  sparkling  wit,  must  instruct  and  amuse  to  the  end  of  time  : 
and,  as  against  error,  we  repeat  that  Bacon  is  soundly  wise,  so  far 
as  he  goes.  There  is  hardly  a  form  of  human  error  within  his 
scope  which  he  did  not  detect,  expose,  and  attach  to  a  satirical 
metaphor  which  never  ceases  to  sting.  He  is  largely  indebted  to 
a  very  extensive  reading  ;  but  the  thoughts  of  others  fall  into  his 
text  with  such  a  close-fitting  compactness  that  he  can  make  even 
the  words  of  the  Sacred  Writers  pass  for  his  own.  A  saying  of 
the  prophet  Daniel,  rather  a  hackneyed  quotation  in  our  day, 
Multi  pertransibunt,  et  augebitur  scientia,  stands  in  the  title-page 
of  the  first  edition  of  Montucla's  '  History  of  Mathematics '  as  a 
quotation  from  Bacon — and  it  is  not  the  only  place  in  which  this 
mistake  occurs.  When  the  truth  of  the  matter,  as  to  Bacon's 
system,  is  fully  recognized,  we  have  little  fear  that  there  will  be 
a  reaction  against  the  man.  First,  because  Bacon  will  always 
live  to  speak  for  himself,  for  he  will  not  cease  to  be  read  : 
secondly,  because  those  who  seek  the  truth  will  find  it  in  the 
best  edition  of  his  works,  and  will  be  most  ably  led  to  know  what 
Bacon  was,  in  the  very  books  which  first  showed  at  large  what  he 
was  not. 

In  this  year  (1620)  appeared  the  corrections  under  which  the 
Congregation  of  the  Index  —  i.e.  the  Committee  of  Cardinals 
which  superintended  the  Index  of  forbidden  books — proposed  to 
allow  the  work  of  Copernicus  to  be  read.  I  insert  these  con- 
ditions in  full,  because  they  are  often  alluded  to,  and  I  know  of 
no  source  of  reference  accessible  to  a  twentieth  part  of  those  who 
take  interest  in  the  question. 

By  a  decree  of  the  Congregation  of  the  Index,  dated  March  5, 
1616,  the  work  of  Copernicus,  and  another  of  Didacus  Astunica, 
are  suspended  donee  coirigantur,  as  teaching  : 

'  Falsam  iilam  doctrinam  Pythagoricam,divinae  que  Scripturje  omnino 
adversantem,  de  mobilitate  Terras  et  immobilitate  Solis.' 

But  a  work  of  the  Carmelite  Foscarini  is  : 

'  Omnino  prohibendura  atque  damnandum,' because  'ostendere  conatur 
prasfatani  doctrinam  ....  consonam  esse  veritati  et  non  adversari 
Sacra3  Sci-iptura3.' 

Works  which   teach  the  false  doctrine  of  the  earth's  motion 


58  A  BUDGET  OF  PARADOXES. 

are  to  be  corrected  ;  those  which  declare  the  doctrine  conformable 
to  Scripture  are  to  be  utterly  prohibited. 

In  a  ;  Monitum  ad  Nicolai  Copernici  lectorem,  ej  usque  emen- 
datio,  permissio,  et  correctio,'  dated  1620  without  the  month  or 
day,  permission  is  given  to  reprint  the  work  of  Copernicus  with 
certain  alterations  ;  and,  by  implication,  to  read  existing  copies 
after  correction  in  writing.  In  the  preamble  the  author  is  called 
nobilia  astrologua  ;  not  a  compliment  to  his  birth,  which  was 
humble,  but  to  his  fame.  The  suspension  was  because  : 

'  Sacree  Scriptures,  ejusque  verro  et  CatLolices  interpretation!  repug- 
nantia  (quod  in  horaine  Christiano  minime  tolerandum)  non  per  hypo- 
thesin  tractare,  sed  ut  verissima  adatruere  noa  dubitat  ! 

And  the  corrections  relate  : 

'  Locis  in  quibus^non  ex  hypothesi,  sed  asserendo  de  situ  et  motu  Terras 
disputat.' 

That  is,  the  earth's  motion  may  be  an  hypothesis  for  eluci- 
dation of  the  heavenly  motions,  but  must  not  be  asserted  as  a 
fact. 


(In  Pref.  circa  finem.)  '  Copernicus.  Si  fortasse  erunt 
qui  cum  omnium  Mathematum  ignari  sint,  tamen  de  illis  judicium  sibi 
summunt,  propter  aliquem  locum  scriptures,  male  ad  suum  propositum 
detortum,  ausi  fuerint  meum  hoc  institutum  reprehendere  ac  insec- 
tari  :  illos  nihil  moror  adeo  ut  etiam  illorum  judicium  tanquam 
temerarium  contemnam.  Non  enim  obscurum  est  Lactantium,  celebrem 
alioqui  scriptorem,  sed  Mathematicum  pai*um,  admodum  pueriliter  de 
forma  terree  loqui,  cum  deridet  eos,  qui  terrain  globi  formam  habere 
prodiderunt.  Itaque  non  debet  mirum  videri  stndiosis,  si  qui  tales  nos 
etiam  videbunt.  Mathemata  Mathematicis  scribuntur,  quibus  et  hi 
nostri  labores,  si  me  non  fallit  opinio,  videbuntur  etiam  Beipub.  eccle- 
siasticee  conducere  aliquid  .  .  .  Emend.  Ibi  si  fortasse  dele  omnia, 
usque  ad  verbum  hi  nostri  labores  et  sic  accommoda  —  Cceterum  hi  nostri 
labores.1 

All  the  allusion  to  Lactantius,  who  laughed  at  the  notion  of  the 
earth  being  round,  which  was  afterwards  found  true,  is  to  be 
struck  out. 

(Cap.  5.  lib.  i.  p.  8.)  '  Copernicus.  Si  tamen  attentius  rem  consider- 
emus,  videbitur  heec  queestio  nondum  absoluta,  et  idcirco  minime 
contemnenda.  Emend.  Si  tamen  attentius  rem  consideremus,  nihil 
refert  an  Terrain  in  medio  Mundi,  an  extra  Medium  existere,  quoad  sol- 
yendas  coelestium  motuum  apparentias  existimemus.' 

We  must  not  say  the  question  is  not  yet  settled,  but  only  that 


COPERNICUS  AND  THE  POPE.  59 

it  may  be  settled  either  way,  so  far  as  mere  explanation  of  the 
celestial  motions  is  concerned. 

(Cap.  8.  lib.  i.)  '  Totum  hoc  caput  potest  expungi,  quia  ex  professo 
tractat  de  veritate  motus  Terree,  dum  solvit  veterum  rationes  probantes 
ejus  quietem.  Cam  tamen  problematice  videatur  loqui ;  ut  studiosis 
satisfiat,  seriesque  et  ordo  libri  integer  maneat ;  emendetur  ut  infra.' 

A  chapter  which  seems  to  assert  the  motion  should  perhaps  be 
expunged  ;  but  it  may  perhaps  be  problematical ;  and,  not  to 
break  up  the  book,  must  be  amended  as  below. 

(p.  6.)  '  Ooperniciis.  Cui  ergo  hesitamus  adhuc,  nobilitatem  illi  formes 
sues  a  natura  congruentem  concedere,  magisquam  quod  totus  labatur 
mundus,  cujus  finis  ignoratur,  soirique  nequit,  neque  fateamur  ipsius 
cotidian®  revolutionis  in  coelo  apparentiam  esse,  et  in  terra  veritatem  ? 
Efc  heec  perinde  se  habere,  ac  si  diceret  Virgilianus  ^Eneas  :  Provehimur 
portu  ....  Emend.  Cur  ergo  non  possum  mobilitatem  illi  formsa 
sues  concedere,  magisque  quod  totus  labatur  mundus,  cujus  finis 
ignoratur  scirique  nequit,  et  quse  apparent  in  coelo,  perinde  se  habere, 
ao  si  .  .  .  .' 

'  Why  should  we  hesitate  to  allow  the  earth's  motion,'  must  be 
altered  into  '  I  cannot  concede  the  earth's  motion.' 

(p.  7.)  '  Copernicus.  Addo  etiam,  quod  satis  absurdum  videretur, 
continent!  sive  locanti  motnm  adscribi,  et  non  potius  contento  et 
locato,  quod  est  terra.  Emend.  Addo  etiam  difficilius  non  esse 
contento  et  locato,  quod  est  Terra,  motum  adscribere,  quam  continenti.' 

We  must  not  say  it  is  absurd  to  refuse  motion  to  the  contained 
and  located,  and  to  give  it  to  the  containing  and  locating ;  say 
that  neither  is  more  difficult  than  the  other. 

(p.  7.)  '  Copernicus.  Vides  ergo  quod  ex  his  omnibus  probabilior  sit 
mobilitas  Terras,  quam  ejus  quies,  preesertim  in  cotidiana  revolutione, 
tanquam  terne  maxime  propria.  EincmL  Vides  .  .  .  delendus  est 
usque  ad  finem  capitis.' 

Strike  out  the  whole  of  the  chapter  from  this  to  the  end ;  it 
says  that  the  motion  of  the  earth  is  the  most  probable  hypothesis. 

(Cap.  9.  lib.  i.  p.  7.)  '  Copernicus.  Cum  igitur  nihil  prohibeat  mobili- 
tatem Teme,  videndum  nunc  arbitror,  an  etiam  plures  illi  motua 
conveniant,  ut  possit  una  errantium  syderum  existimari.  Emend.  Cum 
igitur  Terram  moveri  assumpserim,  videndum  nunc  arbitror,  an  etiam 
illi  plures  possint  convenire  motus.' 

We  must  not  say  that  nothing  prohibits  the  motion  of  the 
earth,  only  that  having  assumed  it,  we  may  inquire  whether  our 
explanations  require  several  motions. 


60  A  BUDGET  OF  PARADOXES. 

(Cap.  10.  lib.  1.  p.  9.)  '  Copernicus.  Non  pudet  nosfateri  ....  hoc 
potius  in  mobilitate  terra?  verificari.  Emend.  ISTon  pudet  nos  assumere 
....  hoc  consequent er  in  mobilitate  verificari.' 

(Cap.  10.  lib.  i.  p.  10.)  '  Copernicus.  Tanta  nimiruni.  est  divina  ha3C 
Opt.  Max.  fabrica.  Emend.  Dele  ilia  verba  postrema.' 

(Cap.  ii.  lib.  i.)  '  Copernicus.  De  triplici  motu  telluris  demonstratio. 
Emend.  De  hypothesi  triplicis  motus  Terree,  ejusque  demonstratioiie.' 

(Cap.  10.  lib.  iv.  p.  122.)  '  Copernicus.  De  magnitudine  horum  trium 
siderum,  Solis,  Lunee,  et  Terrse.  Emend.  Dele  verba  horum  trium 
sidcrum,  quia  terra  non  est  sidus,  ut  facit  earn  Copernicus. ' 

We  must  not  say  we  are  not  ashamed  to  acknowledge ;  assume 
is  the  word.  We  must  not  call  this  assumption  a  Divine  work. 
A  chapter  must  not  be  headed  demonstration,  but  hypothesis. 
The  earth  must  not  be  called  a  star ;  the  word  implies  motion. 

It  will  be  seen  that  it  does  not  take  much  to  reduce  Copernicus 
to  pure  hypothesis.  No  personal  injury  being  done  to  the  author 
—  who  indeed  had  been  1 7  years  out  of  reach — the  treatment  of 
his  book  is  now  an  excellent  joke.  It  is  obvious  that  the  Car- 
dinals of  the  Index  were  a  little  ashamed  of  their  position,  and 
made  a  mere  excuse  of  a  few  corrections.  Their  mode  of  deal- 
ing with  chap.  8,  this problematice  videtur  loqui,ut  studiosis  satis- 
fiat,  is  an  excuse  to  avoid  corrections.  But  they  struck  out  the 
stinging  allusion  to  Lactantius  in  the  preface,  little  thinking, 
honest  men,  for  they  really  believed  what  they  said — that  the 
light  of  Lactantius  would  grow  dark  before  the  brightness  of 
their  own. 

1622.  I  make  no  reference  to  the  case  of  Galileo,  except  this. 
I  have  pointed  out  (Penny  Cycl.  Suppl.  '  Gralileo  ; '  Engl.  Cycl. 
'  Motion  of  the  Earth ')  that  it  is  clear  the  absurdity  was  the  act 
of  the  Italian  Inquisition — for  the  private  and  personal  pleasure 
of  the  Pope,  who  knew  that  the  course  he  took  would  not  commit 
him  as  Pope — and  not  of  the  body  which  calls  itself  the  Church. 
Let  the  dirty  proceeding  have  its  right  name.  The  Jesuit 
Riccioli,  the  stoutest  and  most  learned  Anti-Copernican  in 
Europe,  and  the  Puritan  Wilkins,  a  strong  Copernican  and 
Pope-hater,  are  equally  positive  that  the  Eoman  Church  never 
pronounced  any  decision  :  and  this  in  the  time  immediately  fol- 
lowing the  ridiculous  proceeding  of  the  Inquisition.  In  like 
manner  a  decision  of  the  Convocation  of  Oxford  is  not  a  law  of 
the  English  Church ;  which  is  fortunate,  for  that  Convocation, 
in  1622,  came  to  a  decision  quite  as  absurd,  and  a  great  deal 
more  wicked  than  the  declaration  against  the  motion  of  the  earth. 
The  second  was  a  foolish  mistake  :  the  first  was  a  disgusting 


KNIGHT  AND  THE  OXFORD  CONVOCATION.  61 

surrender  of  right  feeling.  Tbe  story  is  told  without  disappro- 
bation by  Anthony  Wood,  who  never  exaggerated  anything 
against  the  university  of  which  he  is  writing  eulogistic  history. 

In  1622,  one  William  Knight  put  forward  in  a  sermon  preached 
before  the  University  certain  theses  which,  looking  at  the  state 
of  the  times,  may  have  been  improper  and  possibly  of  seditious 
intent.  One  of  them  was  that  the  bishop  might  excommunicate 
the  civil  magistrate  :  this  proposition  the  clerical  body  could  not 
approve,  and  designated  it  by  the  term  erronea,  the  mildest 
going.  But  Knight  also  declared  as  follows — 

Stibditis  mere  privatis,  si  Tyrannus  tanquarn  latro  aut  stuprator 
in  ipsos  faciat  impetum,  et  ipsi  nee  potestatem  ordinariam 
implorare,  nee  alia  ratione  effugere  periculum  possint,  in  preserti 
periculo  se  et  suos  contra  tyrannum,  sicut  contra  privatum  gras- 
satorem,  defendere  licet. 

That  is,  a  man  may  defend  his  purse  or  a  woman  her  honour, 
against  the  personal  attack  of  a  king,  as  against  that  of  a  private 
person,  if  no  other  means  of  safety  can  be  found.  The  Convoca- 
tion sent  Knight  to  prison,  declared  the  proposition  'falsa, 
periculosa,  et  impiaj  and  enacted  that  all  applicants  for  degrees 
should  subscribe  this  censure,  and  make  oath  that  they  would 
neither  hold,  teach,  nor  defend  Knight's  opinions. 

The  thesis,  in  the  form  given,  was  unnecessary  and  improper. 
Though  strong  opinions  of  the  king's  rights  were  advanced  at  the 
time,  yet  no  one  ventured  to  say  that,  ministers  and  advisers 
apart,  the  king  might  personally  break  the  law ;  and  we  know 
that  the  first  and  only  attempt  which  his  successor  made  brought 
on  the  crisis  which  cost  him  his  throne  and  his  head.  But  the 
declaration  that  the  proposition  was  false  far  exceeds  in  all  that 
is  disreputable  the  decision  of  the  Inquisition  against  the  earth's 
motion.  We  do  not  mention  this  little  matter  in  England. 
Knight  was  a  Puritan,  and  Neal  gives  a  short  account  of  his  ser- 
mon. From  comparison  with  Wood,  I  judge  that  the  theses,  as 
given,  were  not  Knight's  words,  but  the  digest  which  it  was 
customary  to  make  in  criminal  proceedings  against  opinion. 
This  heightens  the  joke,  for  it  appears  that  the  qualifiers  of  the 
Convocation  took  pains  to  present  their  condemnation  of  Knight 
in  the  terms  which  would  most  unequivocally  make  their  censure 
condemn  themselves.  This  proceeding  took  place  in  the  interval 
between  the  two  proceedings  against  Gralileo  :  it  is  left  undeter- 
mined whether  we  must  say  pot-kettle-pot  or  kettle-pot-kettle. 


62  A  BUDGET   OF  PARADOXES. 

Liberti  Fromondi  .  .  '.  Ant-Aristarchus,  sive  orbis  terras  immo- 
bilis.  Antwerp,  1631,  8vo. 

This  book  contains  the  evidence  of  an  ardent  opponent  of 
Galileo  to  the  fact,  that  Eoman  Catholics  of  the  day  did  not  con- 
sider the  decree  of  the  Index  or  of  the  Inquisition  as  a  declara- 
tion of  their  Church.  Fromond  would  have  been  glad  to  say  as 
much,  and  tries  to  come  near  it,  but  confesses  he  must  abstain. 
See  Penny  Cyclop.  Suppl.  'Galileo,'  and  Eng.  Cycl.  'Motion 
of  the  Earth.'  The  author  of  a  celebrated  article  in  the  Dublin 
Review,  in  defence  of  the  Church  of  Eome,  seeing  that  Drink- 
water  Bethune  makes  use  of  the  authority  of  Fromondus,  but  for 
another  purpose,  sneers  at  him  for  bringing  up  a  '  musty  old  Pro- 
fessor.' If  he  had  known  Fromondus,  and  used  him  he  would  have 
helped  his  own  case,  which  is  very  meagre  for  want  of  knowledge.1 

Advis  a  Monseigneur  1'eminentissime  Cardinal  Due  de  Richelieu, 
siir  la  Proposition  faicte  par  le  Sieur  Morin  pour  1'invention  des 
longitudes.  Paris,  1634,  8vo. 

This  is  the  Official  Eeport  of  the  Commissioners  appointed  by 
the  Cardinal,  of  whom  Pascal  is  the  one  now  best  known,  to  consider 
Morin's  plan.  See  the  full  account  in  Delambre,  Hist.  Astr. 
Mod.  ii.  236,  &c. 

Arithmetica  et  Greometria  practica.  By  Adrian  Metius.  Ley- 
den,  1640,  4to. 

This  book  contains  the  celebrated  approximation  guessed  at  by 
his  father,  Peter  Metius,  namely,  that  the  diameter  is  to  the 
circumference  as  113  to  355.  The  error  is  at  the  rate  of  about  a 
foot  in  2,000  miles.  Peter  Metius,  having  his  attention  called 
to  the  subject  by  the  false  quadrature  of  Duchesne,  found  that 
the  ratio  lay  between  ^-5-  and  f|£.  He  then  took  the  liberty  of 
taking  the  mean  of  both  numerators  and  denominators,  giving 
44JJ-  He  had  no  right  to  presume  that  this  mean  was  better  than 
either  of  the  extremes ;  nor  does  it  appear  positively  that  he  did  so. 
He  published  nothing :  but  his  son  Adrian,  when  Van  Ceulen's  work 
showed  how  near  his  father's  result  came  to  the  truth,  first  made 
it  known  in  the  work  above.  (See  Eng.  Cyclop,  art. '  Quadrature.') 

A  discourse  concerning  a  new  world  and  another  planet,  in  two 

books.     London,  1640,  8vo. 
Cosmotheoros :    or  conjectures  concerning  the  planetary  worlds 

1  The  article  referred  to  is  about  thirty  years  old  :  since  it  appeared  another  has 
been  given  (Dubl.  Rev.  Sept.  1865)  which  is  of  much  greater  depth.  In  it  will  also  bo 
found  the  Roman  view  of  Bishop  Virgil  (ante,  p.  24). 


PLUEALITY   OF   WORLDS.  63 

and  their  inhabitants.  Written  in  Latin,  by  Christianus  Huy- 
ghens.  This  translation  was  first  published  in  1698.  Glasgow 
1757,  8vo.  [The  original  is  also  of  1698.] 

The  first  work  is  by  Bishop  Wilkins,  being  the  third  edition,  [first 
in  1638]  of  the  first  book,  'That  the  Moon  maybe  a  Planet;'  and  the 
first  edition  of  the  second  work,  '  That  the  Earth  may  be  a  Planet.' 
[See  more  under  the  reprint  of  1802.]  Whether  other  planets  be 
inhabited  or  not,  that  is,  crowded  with  organisations,  some  of 
them  having  consciousness,  is  not  for  me  to  decide ;  but  I  should 
be  much  surprised  if,  on  going  to  one  of  them,  I  should  find  it 
otherwise.  The  whole  dispute  tacitly  assumes  that,  if  the  stars 
and  planets  be  inhabited,  it  must  be  by  things  of  which  we  can 
form  some  idea.  But  for  aught  we  know,  what  number  of  such 
bodies  there  are,  so  many  organisms  may  there  be,  of  which  we 
have  no  way  of  thinking  nor  of  speaking.  This  is  seldom  re- 
membered. In  like  manner  it  is  usually  forgotten  that  the  matter 
of  other  planets  may  be  of  different  chemistry  from  ours.  There 
may  be  no  oxygen  and  hydrogen  in  Jupiter,  which  may  have  gens 
of  its  own.  But  this  must  not  be  said  :  it  would  limit  the  omni- 
science of  the  a  priori  school  of  physical  inquirers,  the  larger  half 
of  the  whole,  and  would  be  very  unphilosophical.  Nine-tenths 
of  my  best  paradoxers  come  out  from  among  this  larger  half, 
because  they  are  just  a  lit/tie  more  than  of  it  at  their  entrance. 

There  was  a  discussion  on  the  subject  some  years  ago,  which 
began  with — 

The  plurality  of  worlds  :  an  Essay.  London,  1853,  8vo.  [By  Dr. 
Wm.  Whewell,  Master  of  Trinity  College,  Cambridge].  A 
dialogue  on  the  plurality  of  worlds,  being  a  supplement  to  the 
Essay  on  that  subject.  [First  found  in  the  second  edition,  1854 ; 
removed  to  the  end  in  subsequent  editions,  and  separate  copies 
issued.] 

A  work  of  sceptical  character,  insisting  on  analogies  which  pro- 
hibit the  positive  conclusion  that  the  planets,  stars,  &c.,  are  what 
we  should  call  inhabited  worlds.  It  produced  several  works  and 
a  large  amount  of  controversy  in  reviews.  The  last  predecessor 
of  whom  I  know  was — 

Plurality  of  Worlds.  .   .  .  By  Alexander  Maxwell.  Second  Edition. 

London,  1820,  8vo. 

This  work  is  directed  against  the  plurality  by  an  author  who 
does  not  admit  modern  astronomy.  It  was  occasioned  by  Dr.  Chal- 
mers's celebrated  discourses  on  religion  in  connexion  with  astro- 
nomy. The  notes  contain  many  citations  on  the  gravity  controversy, 


64  A  BUDGET   OF  PAEADOXES. 

from  authors  now  very  little  read  :  and  this  is  its  present  value.  I 
find  no  mention  of  Maxwell,  not  even  in  Watt.  He  communicated 
with  mankind  without  the  medium  of  a  publisher ;  and,  from  Vieta 
till  now,  this  method  has  always  been  favourable  to  loss  of  books. 

A  correspondent  informs  me  that  Alex.  Maxwell,  who  wrote  on 
the  plurality  of  worlds,  in  1820,  was  a  law-bookseller  and  pub- 
lisher (probably  his  own  publisher)  in  Bell  Yard.  He  had  pecu- 
liar notions,  which  he  was  fond  of  discussing  with  his  customers. 
He  was  a  bit  of  a  Swedenborgian. 

There  is  a  class  of  hypothetical  creations  which  do  not  belong 
to  my  subject,  because  they  are  acknowledged  to  be  fictions,  as 
those  of  Lucian,  Eabelais,  Swift,  Francis  Godwin,  Voltaire,  &c. 
All  who  have  more  positive  notions  as  to  either  the  composition 
or  organisation  of  other  worlds,  than  the  reasonable  conclusion 
•that  our  Architect  must  be  quite  able  to  construct  millions  of 
other  buildings  on  millions  of  other  plans,  ought  to  rank  with 
the  writers  just  mentioned,  in  all  but  self-knowledge.  Of  every 
one  of  their  systems  I  say,  as  the  Irish  Bishop  said  of  Gulliver's 
book, — I  don't  believe  half  of  it.  Huyghens  had  been  preceded 
by  Fontenelle,  who  attracted  more  attention.  Huyghens  is  very 
fanciful  and  very  positive  ;  but  he  gives  a  true  account  of  his 
method.  '  But  since  there's  no  hopes  of  a  Mercury  to  carry  us 
such  a  journey,  we  shall  e'en  be  contented  with  what's  in  our 
power :  we  shall  suppose  ourselves  there.  .  .  .'  And  yet  he  says, 
— 'We  have  proved  that  they  live  in  societies,  have  hands  and 
feet.  .  .  .'  Kircher  had  gone  to  the  stars  before  him,  but  would 
not  find  any  life  in  them,  either  animal  or  vegetable. 

The  question  of  the  inhabitants  of  a  particular  planet  is  one 
which  has  truth  on  one  side  or  the  other  :  either  there  are  some 
inhabitants,  or  there  are  none.  Fortunately,  it  is  of  no  conse- 
quence which  is  true.  But  there  are  many  cases,  where  the 
balance  is  equally  one  of  truth  and  falsehood,  in  which  the  choice 
is  a  matter  of  importance.  My  work  selects,  for  the  most  part, 
sins  against  demonstration  :  but  the  world  is  full  of  questions  of 
fact  or  opinion,  in  which  a  struggling  minority  will  become  a 
majority,  or  else  will  be  gradually  annihilated  :  and  each  of  the 
cases  subdivides  into  results  of  good,  and  results  of  evil.  What  is 
to  be  done  ? 

Periculosum  est  credere  et  non  credere ; 
Hippolitus  obiit  quia  novercee  creditum  est ; 
Cassandrse  quia  non  creditum  ruit  Ilium  : 
Ergo  exploranda  est  veritas  multum  prius 
Quam  stulta  prove  judicet  sententia. 


VENETIAN  PAKADOXERS.   LONGOMONTANUS.        65 


Nova  Demonstratio  immobilitatis  terraB  petita  ex  virtute  mag- 
netica.  Bj  Jacobus  Grandamicus.  Flcxiae  (La  Fleche),  1645, 
4*o. 

No  magnetic  body  can  move  about  its  poles :  the  earth  is  a 
magnetic  body,  therefore,  &c.  The  iron  and  its  magnetism  are 
typical  of  two  natures  in  one  person  ;  so  it  is  said,  '  Si  exaltatus 
fuero  a  terra,  omnia  traham  ad  me  ipsum.' 

Le  glorie  degli  incogniti,  o  vero  gli  huomini  illustri  dell'  ac- 
cademia  de'  signer!  incogniti  di  Venetia.  Venice,  1 647,  4to. 

This  work  is  somewhat  like  a  part  of  my  own  :  it  is  a  budget 
of  Venetian  nobodies  who  wished  to  be  somebodies  ;  but  paradox 
is  not  the  only  means  employed.  It  is  of  a  serio-comic  character, 
gives  genuine  portraits  in  copper-plate,  and  grave  lists  of  works ; 
but  satirical  accounts.  The  astrologer  Andrew  Argoli  is  there, 
and  his  son  ;  both  of  whom,  with  some  of  the  others,  have  place  in 
modern  works  on  biography.  Argoli's  discovery  that  logarithms 
facilitate  easy  processes,  but  increase  the  labour  of  difficult  ones, 
is  worth  recording. 

Controversiae   de  vera   circuli   mensura  .  .  .    inter 

C.  S.  Longomontanum  et  Jo.  Pellium.    Amsterdam,  1647,  4to. 

Longomontanus,  a  Danish  astronomer  of  merit,  squared  the 
circle  in  1644  :  he  found  out  that  the  diameter  43  gives  the  square 
root  of  18252  for  the  circumference;  which  gives  3*14185  .  .  . 
for  the  ratio.  Pell  answered  him,  and  being  a  kind  of  circulating 
medium,  managed  to  engage  in  the  controversy  names  known  and 
unknown,  as  Koberval,  Hobbes,  Carcavi,  Lord  Charles  Cavendish, 
Pallieur,  Mersenne,  Tassius,  Baron  Wolzogen,  Descartes,  Cavalieri 
and  Grolius.  Among  them,  of  course,  Longomontanus  was  made 
mincemeat :  but  he  is  said  to  have  insisted  on  the  discovery  in  his 
epitaph. 

The  great  circulating  mediums,  who  wrote  to  everybody,  heard 
from  everybody,  and  sent  extracts  to  everybody  else,  have  been 
Father  Mersenne,  John  Collins,  and  the  late  Prof.  Schumacher : 
all  'late'  no  doubt,  but  only  the  last  recent  enough  to  be  so 
styled.  If  M.C.S.  should  ever  again  stand  for  '  Member  of  the 
Corresponding  Society,'  it  should  raise  an  acrostic  thought  of  the 
three.  There  is  an  allusion  to  Mersenne's  occupation  in  Hobbes's 
reply  to  him.  He  wanted  to  give  Hobbes,  who  was  very  ill  at 
Paris,  the  Roman  Eucharist :  but  Hobbes  said,  'I  have  settled  all 

F 


QQ  A  BUDGET   OF  PARADOXES. 

that  long  ago ;  when  did  you  hear  from  Grassendi  ?'  We  are  re- 
minded of  William's  answer  to  Burnet.  John  Collins  disseminated 
Newton,  among  others.  Schumacher  ought  to  have  been  called 
the  postmaster-general  of  astromony,  as  Collins  was  called  the 
attorney-general  of  mathematics. 

A  late  discourse.  ...  by  Sir  Kenelme  Digby  .  .  .  Rendered  into 
English  by  R.  White.     London,  1658,  12mo. 

On  this  work  see  Notes  and  Queries,  2nd  series,  vii.  231,  299, 
445,  viii.  190.  It  contains  the  celebrated  sympathetic  powder.  I 
am  still  in  much  doubt  as  to  the  connexion  of  Digby  with  this 
tract.  Without  entering  on  the  subject  here,  I  observe  that  in 
Birch's  'History  of  the  Royal  Society,'  to  which  both  Digby  and 
White  belonged,  Digby,  though  he  brought  many  things  before 
the  Society,  never  mentioned  the  powder,  which  is  connected  only 
with  the  names  of  Evelyn  and  Sir  Gilbert  Talbot.  The  sym- 
pathetic powder  was  that  which  cured  by  anointing  the  weapon 
with  its  salve  instead  of  the  wound.  I  have  long  been  convinced 
that  it  was  efficacious.  The  directions  were  to  keep  the  wound 
clean  and  cool,  and  to  take  care  of  diet,  rubbing  the  salve  on  the 
knife  or  sword.  If  we  remember  the  dreadful  notions  upon  drugs 
which  prevailed,  both  as  to  quantity  and  quality,  we  shall  readily 
see  that  any  way  of  not  dressing  the  wound  would  have  been  use- 
ful. If  the  physicians  had  taken  the  hint,  had  been  careful  of 
diet,  &c. ,  and  had  poured  the  little  barrels  of  medicine  down  the 
throat  of  a  practicable  doll,  they  would  have  had  their  magical 
cures  as  well  as  the  surgeons.  Matters  are  much  improved  now  ; 
the  quantity  of  medicine  given,  even  by  orthodox  physicians, 
would  have  been  called  infinitesimal  by  their  professional  ances- 
tors. Accordingly,  the  College  of  Physicians  has  a  right  to 
abandon  its  motto,  which  is  Ars  longa,  vita  brevis,  meaning 
Practice  is  long,  so  life  is  short. 

Examinatio  et  emendatio  Mathematics  Hodiernse.     By  Thomas 
Hobbes.     London.  1666,  4to. 

In  six  dialogues  :  the  sixth  contains  a  quadrature  of  the  circle. 
But  there  is  another  edition  of  this  work,  without  place  or  date 
on  the  title-page,  in  which  the  quadrature  is  omitted.  This 
seems  to  be  connected  with  the  publication  of  another  quadra- 
ture, without  date,  but  about  1670,  as  may  be  judged  from  its 
professing  to  answer  a  tract  of  Wallis,  printed  in  1669.  The 
title  is  '  Quadratura  circuli,  cubatio  sphaBroe,  duplicatio  cubi,'  4to . 


THOMAS   HOBBES.      SCALIGER.  67 

Hobbes,  who  began  in  1655,  was  very  wrong  in  his  quadrature  ; 
but,  though  not  a  Gregory  St.  Vincent,  he  was  not  the  ignoramus 
in  geometry  that  he  is  sometimes  supposed.  His  writings,  erro- 
neous as  they  are  in  many  things,  contain  acute  remarks  on  points 
of  principle.  He  is  wronged  by  being  coupled  with  Joseph 
Scaliger,  as  the  two  great  instances  of  men  of  letters  who  have 
come  into  geometry  to  help  the  mathematicians  out  of  their  diffi- 
culty. I  have  never  seen  Scaliger's  quadrature,  except  in  the 
answers  of  Adrianus  Eomanus,  Vieta  and  Clavius,  and  in  the 
extracts  of  Kastner.  Scaliger  had  no  right  to  such  strong  oppo- 
nents :  Erasmus  or  Bentley  might  just  as  well  have  tried  the 
problem,  and  either  would  have  done  much  better  in  any  twenty 
minutes  of  his  life. 

Scaliger  inspired  some  mathematicians  with  great  respect  for 
his  geometrical  knowledge.  Vieta,  the  first  man  of  his  time,  who 
answered  him,  had  such  regard  for  his  opponent  as  made  him 
conceal  Scaliger's  name.  Not  that  he  is  very  respectful  in  his 
manner  of  proceeding  :  the  following  dry  quiz  on  his  opponent's 
logic  must  have  been  very  cutting,  being  true.  '  In  grammaticis, 
dare  navibus  Austros,  et  dare  naves  Austris,  sunt  aeque  significantia. 
Sed  in  Geometricis,  aliud  est  adsumpsisse  circulum  BCD  non  esse 
majorem  triginta  sex  segmentis  BCDF,  aliud  circulo  BCD  non  esse 
majora  trigiuta  sex  segmenta  BCDF.  Ilia  adsumptiuncula  vera  est^ 
hoec  falsa.'  Isaac  Casaubon,  in  one  of  his  letters  to  De  Thou, 
relates  that,  he  and  another  paying  a  visit  to  Vieta,  the  conversa- 
tion fell  upon  Scaliger,  of  whom  the  host  said  that  he  believed 
Scaliger  was  the  only  man  who  perfectly  understood  mathematical 
writers,  especially  the  Greek  ones  :  and  that  he  thought  more  of 
Scaliger  when  wrong  than  of  many  others  when  right  ;  pluris  se 
Scaligerum  vel  errantem  facere  quam  multos  KaropSovvras.  This 
must  have  been  before  Scaliger's  quadrature  (1594).  There  is  an 
old  story  of  some  one  saying, '  Mallem  cum  Scaligero  errare,  quam 
cum  Clavio  recte  sapere.'  This  I  cannot  help  suspecting  to  have 
been  a  version  of  Vieta's  speech  with  Clavius  satirically  inserted, 
on  account  of  the  great  hostility  which  Vieta  showed  towards 
Clavius  in  the  latter  years  of  his  life. 

Montucla  could  not  have  read  with  care  either  Scaliger's  quadra- 
ture or  Clavius's  refutation.  He  gives  the  first  a  wrong  date  :  he 
assures  the  world  that  there  is  no  question  about  Scaliger's  quad- 
rature being  wrong,  in  the  eyes  of  geometers  at  least :  and  he 
states  that  Clavius  mortified  him  extremely  by  showing  that  it 
made  the  circle  less  than  its  inscribed  dodecagon,  which  is,  of 
course,  equivalent  to  asserting  that  a  straight  line  is  not  always 

F   2 


68  A  BUDGET   OF  PARADOXES. 

the  shortest  distance  between  two  points.  Did  Clavius  show 
this  ?  No,  it  was  Scaliger  himself  who  showed  it,  boasted 
of  it,  and  declared  it  to  be  a  '  noble  paradox '  that  a  theorem 
false  in  geometry  is  true  in  arithmetic  ;  a  thing,  he  says  with 
great  triumph,  not  noticed  by  Archimedes  himself!  He  says  in 
so  many  words  that  the  periphery  of  the  dodecagon  is  greater 
than  that  of  the  circle  ;  and  that  the  more  sides  there  are  to  the 
inscribed  figure,  the  more  does  it  exceed  the  circle  in  which  it  is. 
And  here  are  the  words,  on  the  independent  testimonies  of  Clavius 
and  Kastner : — 

Ambitus  dodecagon!  circulo  inscribendi  plus  potest  quam  circuli  am- 
bitus. Et  quanto  deinceps  pluriuin  laterum  fuerit  polygonum  circulo 
inscribendum,  tanto  plus  poterit  ambitus  polygoni  quam  ambitus 
circuli. 

There  is  much  resemblance  between  Joseph  Scaliger  and 
William  Hamilton,  in  a  certain  impetuosity  of  character,  and  in- 
aptitude to  think  of  quantity.  Scaliger  maintained  that  the  arc 
of  a  circle  is  less  than  its  chord  in  arithmetic,  though  greater  in 
geometry  ;  Hamilton  arrived  at  two  quantities  which  are  identi- 
cal, but  the  greater  the  one  the  less  the  other.  But,  on  the  whole, 
I  liken  Hamilton  rather  to  Julius  than  to  Joseph.  On  this  last 
hero  of  literature  I  repeat  Thomas  Edwards,  who  says  that  a  man 
is  unlearned  who,  be  his  other  knowledge  what  it  may,  does  not 
understand  the  subject  he  writes  about.  And  now  one  of  many 
instances  in  which  literature  gives  to  literature  character  in 
science.  Anthony  Teissier,  the  learned  annotator  of  De  Thou's 
biographies,  says  of  Finseus,  '  II  se  vanta  sans  raison  avoir  trouve 
la  quadrature  du  cercle  ;  la  gloire  de  cette  admirable  decouverte 
etait  reservee  a  Joseph  Scaliger,  comme  1'a  ecrit  Scevole  de 
St.  Marthe.' 

Natural  and  Political  Observations  .  .  .  npon  the  Bills  of 
Mortality.  By  John  Graunt,  citizen  of  London.  London,  1662, 
4to. 

This  is  a  celebrated  book,  the  first  great  work  upon  mortality. 
But  the  author,  going  ultra  crepidam,  has  attributed  to  the 
motion  of  the  moon  in  her  orbit  all  the  tremors  which  she  gets 
from  a  shaky  telescope.  But  there  is  another  paradox  about  this 
book  :  the  above  absurd  opinion  is  attributed  to  that  excellent 
mechanist,  Sir  William  Petty,  who  passed  his  days  among  the 
astronomers.  Orraunt  did  not  write  his  own  book  I  Anthony  Wood 
hints  that  Petty  '  assisted,  or  put  into  a  way '  his  old  benefactor : 
no  doubt  the  two  friends  talked  the  matter  over  many  a  time. 


JOHN  GEAUNT.   GADBURY  ON  COMETS.         69 

Burnet  and  Pepys  state  that  Petty  wrote  the  book.  It  is  enough 
for  me  that  Graunt,  whose  honesty  was  never  impeached,  uses  the 
plainest  incidental  professions  of  authorship  throughout ;  that  he 
was  elected  into  the  Eoyal  Society  because  he  was  the  author ; 
that  Petty  refers  to  him  as  author  in  scores  of  places,  and  published 
an  edition,  as  editor,  after  Graunt's  death,  with  Graunt's  name  of 
course.  The  note  on  Graunt  in  the  '  Biographia  Britannica '  may 
be  consulted ;  it  seems  to  me  decisive.  Mr.  C.  B.  Hodge,  an  able 
actuary,  has  done  the  best  that  can  be  done  on  the  other  side  in  the 
Assurance  Magazine,  viii.  234.  If  I  may  say  what  is  in  my  mind, 
without  imputation  of  disrespect,  I  suspect  some  actuaries  have 
a  bias :  they  would  rather  have  Petty  the  greater  for  their  Cory- 
pha3us  than  Graunt  the  less. 

Pepys  is  an  ordinary  gossip :  but  Burnet's  account  has  an  ani- 
mus which  is  of  a  worse  kind.  He  talks  of  '  one  Grraunt,  a  Papist, 
under  whose  name  Sir  William  Petty  published  his  observations 
on  the  bills  of  mortality.'  He  then  gives  the  cock  without  a  bull 
story  of  Graunt  being  a  trustee  of  the  New  River  Company,  and 
shutting  up  the  cocks  and  carrying  off  their  keys,  just  before  the 
fire  of  London,  by  which  a  supply  of  water  was  delayed.  It  was 
one  of  the  first  objections  made  to  Burnet's  work,  that  Graunt  was 
not  a  trustee  at  the  time  ;  and  Maitland,  the  historian  of  London, 
ascertained  from  the  books  of  the  Company  that  he  was  not 
admitted  until  twenty-three  days  after  the  breaking  out  of  the 
fire.  Graunt's  first  admission  to  the  Company  took  place  on  the 
very  day  on  which  a  committee  was  appointed  to  inquire  into  the 
cause  of  the  fire.  So  much  for  Burnet.  I  incline  to  the  view  that 
Graunt's  setting  London  on  fire  strongly  corroborates  his  having 
written  on  the  bills  of  mortality  :  every  practical  man  takes  stock 
before  he  commences  a  grand  operation  in  business. 

De  Cometis :  or  a  discourse  of  the  natures  and  effects  of 
Comets,  as  they  are  philosophically,  historically,  and  astrologi- 
cal^ considered.  With  a  brief  (yet  full)  account  of  the  III  late 
Comets,  or  blazing  stars,  visible  to  all  Europe.  And  what  (in  a 
natural  way  of  judicature)  they  portend.  Together  with  some 
observations  on  the  nativity  of  the  Grand  Seignior.  By  John 
Gadbury,  ^iXo^a^qyuartk-o'c.  London,  1665,  4to. 

Gadbury,  though  his  name  descends  only  in  astrology,  was  a  well- 
informed  astronomer.  D'Israeli  sets  down  Gadbury,  Lilly,  Wharton, 
Booker,  &c.,  as  rank  rogues  :  I  think  him  quite  wrong.  The  easy 
belief  in  roguery  and  intentional  imposture  which  prevails  in 
edueated  society  is,  to  my  mind,  a  greater  presumption  against  the 


70  A  BUDGET   OF  PARADOXES. 

honesty  of  mankind  than  all  the  roguery  and  imposture  itself. 
Putting  aside  mere  swindling  for  the  sake  of  gain,  and  looking  at 
speculation  and  paradox,  I  find  very  little  reason  to  suspect  wilful 
deceit.  My  opinion  of  mankind  is  founded  upon  the  mournful  fact 
that,  so  far  as  I  can  see,  they  find  within  themselves  the  means  of 
believing  in  a  thousand  times  as  much  as  there  is  to  believe  in, 
judging  by  experience.  I  do  not  say  anything  against  Isaac 
D'Israeli  for  talking  his  time.  We  are  all  in  the  team,  and  we  all 
go  the  road,  but  we  do  not  all  draw. 

An  essay  towards  a  real  character  and  a  philosophical  language. 
By  John  Wilkins  [Dean  of  Ripon,  afterwards  Bishop  of 
Chester].  London,  1668,  folio. 

This  work  is  celebrated,  but  little  known.  Its  object  gives  it 
a  right  to  a  place  among  paradoxes.  It  proposes  a  language — if 
that  be  the  proper  name — in  which  things  and  their  relations 
shall  be  denoted  by  signs,  not  words :  so  that  any  person,  what- 
ever may  be  his  mother  tongue,  may  read  it  in  his  own  words. 
This  is  an  obvious  possibility,  and,  I  am  afraid,  an  obvious  im- 
practicability. One  man  may  construct  such  a  system — Bishop 
Wilkins  has  done  it — but  where  is  the  man  who  will  learn  it  ? 
The  second  tongue  makes  a  language,  as  the  second  blow  makes  a 
fray.  There  has  been  very  little  curiosity  about  his  performance, 
the  work  is  scarce  ;  and  I  do  not  know  where  to  refer  the  reader  for 
any  account  of  its  details,  except  to  the  partial  reprint  of  Wilkins 
presently  mentioned  under  1802,  in  which  there  is  an  unsatisfac- 
tory abstract.  There  is  nothing  in  the  '  Biographia  Britannica,' 
except  discussion  of  Anthony  Wood's  statement  that  the  hint  was 
derived  from  Dalgarno's  book,  '  De  Signis,'  1661.  Hamilton 
('  Discussions,'  Art.  5,'  Dalgarno ')  does  not  say  a  word  on  this  point, 
beyond  quoting  Wood  ;  and  Hamilton,  though  he  did  now  and 
then  write  about  his  countrymen  with  a  rough-nibbed  pen,  knew 
perfectly  well  how  to  protect  their  priorities. 

Problema  Austriacum.     Plus  ultra  Quadratura  Circuli.     Auctore 
-  P.   Gregorio  a   Sancto  Vincentio  Soc.    Jesu.,   Antwerp,  1647, 
folio. — Opus  Geometricum  posthumum  ad  Mesolabium.     By  the 
same.     Gandavi  [Ghent],  1668,  folio. 

The  first  book  has  more  than  1200  pages,  on  all  kinds  of 
geometry.  Gregory  St.  Vincent  is  the  greatest  of  circle-squarers, 
and  his  investigations  led  him  into  many  truths  :  he  found  the 
property  of  the  area  of  the  hyperbola  which  led  to  Napier's  loga- 
rithms being  called  hyperbolic.  Montucla  says  of  him,  with  sly 


THE  MESOLABUM.      GEOMETRICAL   QUADRATURE.  71 

truth,  that  no  one  has  ever  squared  the  circle  with  so  much  genius, 
or,  excepting  his  principal  object,  with  so  much  success.  His 
reputation,  and  the  many  merits  of  his  work,  led  to  a  sharp  con- 
troversy on  his  quadrature,  which  ended  in  its  complete  exposure 
by  Huyghens  and  others.  He  had  a  small  school  of  followers, 
who  defended  him  in  print. 

Renati  Francisci  Slusii  Hesolabum.  Leodii  Eburonum  [Liege], 
1668,  4to. 

The  Mesolabum  is  the  solution  of  the  problem  of  finding  two 
mean  proportionals,  which  Euclid's  geometry  does  not  attain. 
Slusius  is  a  true  geometer,  and  uses  the  ellipse,  &c.:  but  he  is 
sometimes  ranked  with  the  trisectors,  for  which  reason  I  place  him 
here,  with  this  explanation. 

The  finding  of  two  mean  proportionals  is  the  preliminary  to  the 
famous  old  problem  of  the  duplication  of  the  cube,  proposed  by 
Apollo  (not  Apollonius)  himself.  D'Israeli  speaks  of  the  '  six 
follies  of  science,' — the  quadrature,  the  duplication,  the  perpetual 
motion,  the  philosopher's  stone,  magic,  and  astrology.  He  might 
as  well  have  added  the  trisection,  to  make  the  mystic  number  seven  : 
but  had  he  done  so,  he  would  still  have  been  very  lenient ;  only 
seven  follies  in  all  science,  from  mathematics  to  chemistry ! 
Science  might  have  said  to  such  a  judge — as  convicts  used  to  say 
who  got  seven  years,  expecting  it  for  life,  '  Thank  you,  my  Lord, 
and  may  you  sit  there  till  they  are  over,' — may  the  Curiosities  of 
Literature  outlive  the  Follies  of  Science ! 

1668.  In  this  year  James  Gregory,  in  his  Vera  Circuli  et 
Hyperbolce  Quadratura,  held  himself  to  have  proved  that  the 
geometrical  quadrature  of  the  circle  is  impossible.  Few  mathe- 
maticians read  this  very  abstruse  speculation,  and  opinion  is 
somewhat  divided.  The  regular  circle-squarers  attempt  the 
arithmetical  quadrature,  which  has  long  been  proved  to  be  impos- 
sible. Very  few  attempt  the  geometrical  quadrature.  One  of 
the  last  is  Malacarne,  an  Italian,  who  published  his  Solution 
Geometrique,  at  Paris,  in  1825.  His  method  would  make  the 
circumference  less  than  three  times  the  diameter. 

La  Geomeh-ie  Frai^oise,  ou  la  Pratique  aisee  ...  La  quadracture 
du  cercle.  Par  le  Sieur  de  Beaulieu,  Ingenieur,  Geographe  du 
Boi  .  .  .  Paris,  1676,  8vo.  [not  Poutault  de  Beaulieu,  the  cele- 
brated topographer  ;  he  died  in  1674]. 

If  this  book  had  been  a  fair  specimen,  I  might  have  pointed 
to  it  in  connection  with  contemporary  English  works,  and  made 


72  A  BUDGET  OF  PAKADOXES. 

a  scornful  comparison.  But  it  is  not  a  fair  specimen.  Beaulieu 
was  attached  to  the  Eoyal  Household,  and  throughout  the  century 
it  may  be  suspected  that  the  household  forced  a  royal  road  to 
geometry.  Fifty  years  before,  Beaugrand,  the  king's  secretary, 
made  a  fool  of  himself,  and  [so  ?]  contrived  to  pass  for  a  geometer. 
He  had  interest  enough  to  get  Desargues,  the  most  powerful 
geometer  of  his  time,  the  teacher  and  friend  of  Pascal,  prohibited 
from  lecturing.  See  some  letters  on  the  History  of  Perspective, 
which  I  wrote  in  the  Athenceum,  in  October  and  November, 
1861.  Montucla,  who  does  not  seem  to  know  the  true  secret  of 
Beaugrand's  greatness,  describes  him  as  '  un  certain  M.  de  Beau- 
grand,  mathematicien,  fort  mal  traite  par  Descartes,  et  a  ce  qu'il 
paroit  avec  justice.' 

Beaulieu's  quadrature  amounts  to  a  geometrical  construction 
which  gives  ?r=  V'lO.  His  depth  may  be  ascertained  from  the 
following  extracts.  First,  on  Copernicus  : — 

Copernic,  Allenaand,  ne  s'esfc  pas  moins  rendu  illustre  par  ses  doctes 
ecrits  ;  et  nous  pourrions  dire  de  luy,  qu'il  seroit  le  seul  et  unique  en 
la  force  de  ses  Problemes,  si  sa  trop  grande  presomption  ne  1'avoit 
porte  a  avancer  en  cette  Science  une  proposition  aussi  absurde,  qu'elle 
est  centre  la  Foy  et  raison,  en  faisant  la  circonference  d'un  Cercle  fixe, 
immobile,  et  le  centre  mobile,  sur  lequel  principe  Geometrique,  il  a 
avance  en  son  Traitte  Astrologique  le  Soleil  fixe,  et  la  Terre  mobile. 

I  digress  here  to  point  out  that  though  our  quadrators,  &c., 
very  often,  and  our  historians  sometimes,  assert  that  men  of  the 
character  of  Copernicus,  &c.  were  treated  with  contempt  and 
abuse  until  their  day  of  ascendancy  came,  nothing  can  be  more 
incorrect.  From  Tycho  Brahe  to  Beaulieu,  there  is  but  one 
expression  of  admiration  for  the  genius  of  Copernicus.  There  is 
an  exception,  which,  I  believe,  has  been  quite  misunderstood. 
Maurolycus,  in  his  'De  Sphaera,'  written  many  years  before  its 
posthumous  publication  in  1575,  and  which  it  is  not  certain  he 
would  have  published,  speaking  of  the  safety  with  which  various 
authors  may  be  read  after  his  cautions,  says,  '  Toleratur  et 
Nicolaus  Copernicus  qui  Solem  fixum  et  Terrain  in  girum 
circumverti  posuit :  et  scutica  potius,  aut  flagello,  quam  repre- 
hensione  dignus  est.'  Maurolycus  was  a  mild  and  somewhat 
contemptuous  satirist,  when  expressing  disapproval :  as  we  should 
now  say,  he  pooh-poohed  his  opponents  ;  but,  unless  the  above 
be  an  instance,  he  was  never  savage  nor  impetuous.  I  am  fully 
satisfied  that  the  meaning  of  the  sentence  is,  that  Copernicus, 
who  turned  the  earth  like  a  boy's  top,  ought  rather  to  have  a  whip 
given  him  wherewith  to  keep  up  his  plaything  than  a  serious 


BEAULIEU'S   ALGEBRA.      SIR  M.  HALE.  73 

refutation.     To  speak  of  tolerating  a  person  as  being  more  worthy 
of  a  flogging  than  an  argument,  is  almost  a  contradiction. 
I  will  now  extract  Beaulieu's  treatise  on  algebra,  entire. 

L'Algebre  est  la  science  curieuse  des  S9avans  et  specialement  d'un 
General  d'Armee  on  Capitaine,  pour  promptement  ranger  une  Armee 
en  bataille,  et  nombre  de  Mousquetaires  et  Piquiers  qui  composent  les 
bataillons  d'icelle,  outre  les  figures  de  I'Arithmetique.  Cette  science  a 
5  figures  particulieres  en  cette  sorte.  P  signifie  plus  au  commerce,  et 
a  1'Armee  Piquiers.  M  signifie  moins,  et  Mousquetaire  en  1'Art  dcs 
bataillons.  [It  is  quite  true  that  P  and  M  were  used  for  plus  and  minus 
in  a  great  many  old  works.]  R  signifie  ratine  en  la  mesure  du  Cube, 
et  en  1'Armee  rang.  Q  signifie  quare  en  Tun  et  1'autre  usage.  C 
signifie  cube  en  la  mesure,  et  Cavallerie  en  la  composition  des  bataillons 
et  escadrons.  Quant  a  1'operation  de  cette  science,  c'est  d'additionner 
un  plus  d'avec  plus,  la  somme  sera  plus,  et  moins  d'avec  plus,  on 
soustrait  le  moindre  du  plus,  etlareste  est  la  somme  requise  ou  nombre 
trouve.  Je  dis  seulement  cecy  en  passant  pour  ceux  qui  n'en  S9avent 
rien  du  tout. 

This  is  the  algebra  of  the  Koyal  Household,  seventy-three  years 
after  the  death  of  Vieta.  Quaere,  is  it  possible  that  the  fame  of 
Vieta,  who  himself  held  very  high  stations  in  the  household  all 
his  life,  could  have  given  people  the  notion  that  when  such  an 
officer  chose  to  declare  himself  an  algebraist,  he  must  be  one 
indeed  ?  This  would  explain  Beaugrand,  Beaulieu,  and  all  the 
beaux.  Beaugrand — not  only  secretary  to  the  king,  but  '  mathe- 
matician '  to  the  Duke  of  Orleans — I  wonder  what  his  'fool 'could 
have  been  like,  if  indeed  he  kept  the  offices  separate, — would 
have  been  in  my  list  if  I  had  possessed  his  Geostatique,  pub- 
lished about  1638.  He  makes  bodies  diminish  in  weight  as  they 
approach  the  earth,  because  the  effect  of  a  weight  on  a  lever  is 
less  as  it  approaches  the  fulcrum. 

Remarks  upon  two  late  ingenious  discourses  .  .  .  By  Dr.  Henry 
More.     London,  1676,  8vo. 

In  1673  and  1675,  Matthew  Hale,  then  Chief  Justice,  published 
two  tracts,  an  '  Essay  touching  Gravitation,'  and  '  Difficiles  Nuga?' 
on  the  Torricellian  experiment.  Here  are  the  answers  by  the 
learned  and  voluminous  Henry  More.  The  whole  would  be 
useful  to  any  one  engaged  in  research  about  ante-Newtonian 
notions  of  gravitation. 


74  A    BUDGET   OF  PABADOXES. 


Observations  touching  the  principles  of  natural  motions  ;  and 
especially  touching  rarefaction  and  condensation  .  .  .  By  the 
author  of  Difficiles  Nugce.  London,  1677,  8vo. 

This  is  another  tract  of  Chief  Justice  Hale,  published  the  year 
after  his  death.  The  reader  will  remember  that  motion,  in  old 
philosophy,  meant  any  change  from  state  to  state  :  what  we  now 
describe  as  motion  was  local  motion.  This  is  a  very  philosophical 
book,  about  flux  and  materia  prima,  virtus  activa  and  essentialis, 
and  other  fundamentals.  I  think  Stephen  Hales,  the  author  of 
the  '  Vegetable  Statics,'  has  the  writings  of  the  Chief  Justice 
sometimes  attributed  to  him,  which  is  very  puny  justice  indeed. 
Matthew  Hale  died  in  1676,  and  from  his  devotion  to  science  it 
probably  arose  that  his  famous  Pleas  of  the  Crown  and  other  law 
works  did  not  appear  until  after  his  death.  One  of  his  con- 
temporaries was  the  astronomer  Thomas  Street,  whose  Caroline 
Tables  were  several  times  printed  :  another  contemporary  was 
his  brother  judge,  Sir  Thomas  Street.  But  of  the  astronomer 
absolutely  nothing  is  known :  it  is  very  unlikely  that  he  and  the 
judge  were  the  same  person,  but  there  is  not  a  bit  of  positive  evi- 
dence either  for  or  against,  so  far  as  can  be  ascertained.  Halley — 
no  less  a  person — published  two  editions  of  the  'Caroline  Tables,'  no 
doubt  after  the  death  of  the  author :  strange  indeed  that  neither 
Halley  nor  any  one  else  should  leave  evidence  that  Street  was 
born  or  died. 

Matthew  Hale  gave  rise  to  an  instance  of  the  lengths  a  lawyer 
will  go  when  before  a  jury  who  cannot  detect  him.  Sir  Samuel 
Shepherd,  the  Attorney  General,  in  opening  Hone's  first  trial, 
calls  him  '  one  who  was  the  most  learned  man  that  ever  adorned 
the  Bench,  the  most  even  man  that  ever  blessed  domestic  life,  the 
most  eminent  man  that  ever  advanced  the  progress  of  science, 
and  one  of  the  [very  moderate]  best  and  most  purely  religious 
men  that  ever  lived. 

Basil  Valentine  his  triumphant  Chariot  of  Antimony,  with 
annotations  of  Theodore  Kirkringius,  M.D.  With  the  true  book 
of  the  learned  Synesius,  a  Greek  abbot,  taken  out  of  the 
Emperour's  library,  concerning  the  Philosopher's  Stone. 
London,  1678,  8vo. 

There  are  said  to  be  three  Hamburg  editions  of  the  collected 
works  of  Valentine,  who  discovered  the  common  antimony,  and 
is  said  to  have  given  the  name  antimoine,  in  a  curious  way. 
Finding  that  the  pigs  of  his  convent  throve  upon  it,  he  gave  it 


BASIL  VALENTINE.      THE  ALCHEMISTS.  75 

to  his  brethren,  who  died  of  it.  The  impulse  given  to  chemistry 
by  E.  Boyle  seems  to  have  brought  out  a  vast  number  of  transla- 
tions, as  in  the  following  tract  :  — 

Collectanea  Chymica  :  A  collection  of  ten  several  treatises  in 
chymistry,  concerning  the  liquor  Alkehest,  the  Mercury  of 
Philosophers,  and  other  curiosities  worthy  the  perusal.  Written 
by  Eir.  Philaletha,  Anonymus,  J.  B.  Van-Helmont,  Dr.  Fr. 
Antonie,  Bernhard  Earl  of  Trevisan,  Sir  Geo.  Bipley,  Rog. 
Bacon,  Geo.  Starkie,  Sir  Hugh  Platt,  and  the  Tomb  of  Semira- 
mis.  See  more  in  the  contents.  London,  1684,  8vo. 

In-  the  advertisements  at  the  ends  of  these  tracts  there  are 
upwards  of  a  hundred  English  tracts,  nearly  all  of  the  per:od, 
and  most  of  them  translations.  Alchemy  looks  up  since  the 
chemists  have  found  perfectly  different  substances  composed  of 
the  same  elements  and  proportions.  It  is  true  the  chemists 
cannot  yet  transmute  ;  but  they  may  in  time  :  they  poke  about 
most  assiduously.  It  seems,  then,  that  the  conviction  that 
alchemy  must  be  impossible  was  a  delusion:  but  we  do  not 
mention  it. 

The  astrologers  and  the  alchemists  caught  it  in  company  in 
the  following,  of  which  I  have  an  unreferenced  note. 

Mendacem  et  futilem  hominem  nominare  qui  volunt,  calenda- 
riographum.  dicunt  ;  at  qui  sceleratum  simul  ac  impostorem, 
chimicum. 

Credo  ratem  rentis,  corpus  ne  crede  chimistis  ; 
Est  qusevis  chimica  tutior  aura  fide. 

Among  the  smaller  paradoxes  of  the  day  is  that  of  the  Times 
newspaper,  which  always  spells  it  chymistry  :  but  so,  I  believe, 
do  Johnson,  Walker,  and  others.  The  Arabic  word  is  very  likely 
formed  from  the  Greek  :  but  it  may  be  connected  either  with 
or  with 


Lettre  d'un  gentil-homme  de  province  a  une  dame  de  qualite, 
sur  le  sujet  de  la  Comete.     Paris,  1681,  4to. 

An  opponent  of  astrology,  whom  I  strongly  suspect  to  have 
been  one  of  the  members  of  the  Academy  of  Sciences  under  the 
name  of  a  country  gentleman,  writes  very  good  sense  on  the 
tremors  excited  by  comets. 


76  A  BUDGET  OF  PARADOXES. 


The  Petitioning- Comet :  or,  a  brief  Chronology  of  all  the  famous 
Comets  and  their  events,  that  have  happened  from  the  birth  of 
Christ  to  this  very  day.  Together  with  a  modest  enquiry  into 
this  present  comet,  London,  1681,  4to. 

A  satirical  tract  against  cometic  prophecy  : — 

'  This  present  comet  (it's  true)  is  of  a  menacing  aspect,  but  if  the 
neiv parliament  (for  whose  convention  so  many  good  men  pray)  continue 
long  to  sit,  I  fear  not  but  the  star  will  lose  its  virulence  and  malignancy, 
or  at  least  its  portent  be  averted  from  this  our  nation ;  which  being 
the  humble  request  to  God  of  all  good  men,  makes  me  thus  entitle  it, 
a  Petitioning-Comet. 

The  following  anecdote  is  new  to  me : — 

Queen  Elizabeth  (1558)  being  then  at  Richmond,  and  being 
disswaded  from  looking  on  a  comet  which  did  then  appear,  made 
answer,  jacta  est  alea,  the  dice  are  thrown ;  thereby  intimating  that 
the  pre-order'd  providence  of  God  was  above  the  influence  of  any  star 
or  comet. 

The  argument  was  worth  nothing :  for  the  comet  might  have 
been  on  the  dice  with  the  event ;  the  astrologers  said  no  more, 
at  least  the  more  rational  ones,  who  were  about  half  of  the 
whole. 

An  astrological  and  theological  discourse  upon  this  present 
great  conjunction  (the  like  whereof  hath  not  (likely)  been  in 
some  ages)  ushered  in  by  a  great  comet.  London,  1682,  4to. 
By  C.  ST. 

The  author  foretells  the  approaching  '  sabbatical  jubilee,'  but 
will  not  fix  the  date :  he  recounts  the  failures  of  his  predeces- 
sors. 

A  judgment  of  the  comet  which  became  first  generally  visible 
to  us  in  Dublin,  December  13,  about  15  minutes  before  5  in  the 
evening,  A.D.  1680.  By  a  person  of  quah'ty.  Dublin,  1682, 
4to. 

The  author  argues  against  cometic  astrology  with  great  ability. 

A  prophecy  on  the  conjunction  of  Saturn  and  Jupiter  in  this 
present  year  1682.  With  some  prophetical  predictions  of  what 
is  likely  to  ensue  therefrom  in  the  year  1684.  By  John  Case, 
Student  in  physic  and  astrology.  London,  1682,  4to. 

According  to  this  writer,  great  conjunctions  of  Jupiter  and 
Saturn  occur  'in  the  fiery  trigon,'  about  once  in  800  years.  Of 


MARCELIS.      MATHEMATICAL   THEOLOGY.  77 

these  there  are  to  be  seven :  six  happened  in  the  several  times 
of  Enoch,  Noah,  Moses,  Solomon,  Christ,  Charlemagne.  The 
seventh,  which  is  to  happen  at  '  the  lamb's  marriage  with  the 
bride,'  seems  to  be  that  of  1682  ;  but  this  is  only  vaguely  hinted. 

De  Quadrature  van  de  Circkel.    By  Jacob  Marcelis.     Amsterdam, 

1698,  4to. 
Ampliatie  en  demonstratie  wegens  de  Quadrature  .  .  .  By  Jacob 

Marcelis.     Amsterdam,  1699,  4to. 
Eenvoudig   vertoog   briev-wys    geschrevem   am    J.    Marcelis  .  . 

Amsterdam,  1702,  4to. 
De  sleutel   en   openinge    van   de  quadrature.    .    .    .   Amsterdam, 

1704,  4to. 

Who  shall  contradict  Jacob  Marcelis  ?     He  says  the  circum- 
ference contains  the  diameter  exactly  times 

0100844908737754167989428218489J4 
6997183037540819440035239271702 

But  he  does  not  come  very  near,  as  the  young  arithmetician  will 
rind. 

Theologiffi  Christianas  Principia  Mathematica.     Auctore  Johanne 
Craig.     London,  1699,  4to. 

This  is  a  celebrated  speculation,  and  has  been  reprinted  abroad, 
and  seriously  answered.  Craig  is  known  in  the  early  history  of 
fluxions,  and  was  a  good  mathematician.  He  professed  to  calcu- 
late, on  the  hypothesis  that  the  suspicions  against  historical 
evidence  increase  with  the  square  of  the  time,  how  long  it  will 
take  the  evidence  of  Christianity  to  die  out.  He  finds,  by 
formulae,  that  had  it  been  oral  only,  it  would  have  gone  out 
A.D.  800 ;  but,  by  aid  of  the  written  evidence,  it  will  last  till 
A.D.  3150.  At  this  period  he  places  the  second  coming,  which  is 
deferred  until  the  extinction  of  evidence,  on  the  authority  of  the 
question  '  When  the  Son  of  Man  cometh,  shall  he  find  faith  on 
the  earth  ?  '  It  is  a  pity  that  Craig's  theory  was  not  adopted  :  it 
would  have  spared  a  hundred  treatises  on  the  end  of  the  world, 
founded  on  no  better  knowledge  than  his,  and  many  of  them 
falsified  by  the  event.  The  most  recent  (October,  1863)  is  a 
tract  in  proof  of  Louis  Napoleon  being  Antichrist,  the  Beast,  the 
eighth  Head,  &c.;  and  the  present  dispensation  is  to  close  soon 
after  1864. 

In  order  rightly  to  judge  Craig,  who  added  speculations  on  the 
variations  of  pleasure  and  pain  treated  as  functions  of  time,  it  is 


78  A  BUDGET   OF  PAEADOXES. 

necessary  to  remember  that  in  Newton's  day  the  idea  of  force,  as  a 
quantity  to  be  measured,  and  as  following  a  law  of  variation,  was 
very  new :  so  likewise  was  that  of  probability,  or  belief,  as  an  object 
of  measurement.  The  success  of  the  '  Principia '  of  Newton  put  it 
into  many  heads  to  speculate  about  applying  notions  of  quantity 
to  other  things  not  then  brought  under  measurement.  Craig 
imitated  Newton's  title,  and  evidently  thought  he  was  making 
a  step  in  advance :  but  it  is  not  every  one  who  can  plough  with 
Samson's  heifer. 

It  is  likely  enough  that  Craig  took  a  hint,  directly  or  in- 
directly, from  Mahometan  writers,  who  make  a  reply  to  the 
argument  that  the  Koran  has  not  the  evidence  derived  from 
miracles.  They  say  that,  as  evidence  of  Christian  miracles  is 
daily  becoming  weaker,  a  time  must  at  last  arrive  when  it  will 
fail  of  affording  assurance  that  they  were  miracles  at  all : 
whence  would  arise  the  necessity  of  another  prophet  and  other 
miracles.  Lee,  the  Cambridge  orientalist,  from  whom  the  above 
words  are  taken,  almost  certainly  never  heard  of  Craig  or  his 
theory. 

Copernicans  of  all  sorts  convicted  ...  to  which  is  added  a  Treatise 
of  the  Magnet.  By  the  Hon.  Bdw.  Howard,  of  Berks.  London, 
1705,  8vo. 

Not  all  the  blood  of  all  the  Howards  will  gain  respect  for  a 
writer  who  maintains  that  eclipses  admit  no  possible  explanation 
under  the  Copernican  hypothesis,  and  who  asks  how  a  man  can 
'  go  200  yards  to  any  place  if  the  moving  superficies  of  the  earth 
does  carry  it  from  him  ? '  Horace  Walpole,  at  the  beginning  of 
his  '  Eoyal  and  Noble  Authors,'  has  mottoed  his  book  with  the 
Cardinal's  address  to  Ariosto,  'Dove  diavolo,  Messer  Ludovico, 
avete  pigliato  tante  coglionerie  ? '  Walter  Scott  says  you  could 
hardly  pick  out,  on  any  principle  of  selection — except  badness 
itself,  he  means  of  course — the  same  number  of  plebeian  authors 
whose  works  are  so  bad.  But  his  implied  satire  on  aristocratic 
writing  forgets  two  points.  First,  during  a  large  period  of  our 
history,  when  persons  of  rank  condescended  to  write,  they  veiled 
themselves  under  'a  person  of  honour,'  '  a  person  of  quality,'  and 
the  like,  when  not  wholly  undescribed.  Not  one  of  these  has 
Walpole  got ;  he  omits,  for  instance,  Lord  Brounker's  translation 
of  Descartes  on  Music.  Secondly,  Walpole  only  takes  the  heads 
of  houses  :  this  cuts  both  ways  ;  he  equally  eliminates  the  Hon. 
Robert  Boyle  and  the  precious  Edward  Howard.  This  last  writer 
is  hardly  out  of  the  time  in  which  aristocracy  suppressed  its 


WHISTON,  DITTOS,  AND   SWIFT.  79 

names ;  the  avowal  was  then  usually  meant  to  make  the  author's 
greatness  useful  to  the  book.  In  our  day,  literary  peers  and 
honourables  are  very  favourably  known,  and  contain  an  eminent 
class.  They  rough  it  like  others,  and  if  such  a  specimen  as  Edw. 
Howard  were  now  to  appear,  he  would  be  greeted  with 

Hereditary  noodle  !  knowest  thou  not, 

Who  would  be  wise,  himself  must  make  him  so  ? 

A  new  and  easy  method  to  find  the  longitude  at  land  or  sea. 
London,  1710,  4to. 

This  tract  is  a  little  earlier  than  the  great  epoch  of  such  publi- 
cations (1714),  and  professes  to  find  the  longitude  by  the  observed 
altitudes  of  the  moon  and  two  stars. 

A  new  method  for  discovering  the  longitude  both  at  sea  and 
land,  humbly  proposed  to  the  consideration  of  the  public.  By 
Wm.  Whiston  and  Humphry  Ditton.  London,  1714,  8vo. 

This  is  the  celebrated  tract,  written  by  the  two  Arian  heretics. 
Swift,  whose  orthodoxy  was  as  undoubted  as  his  meekness,  wrote 
upon  it  the  epigram  if,  indeed,  that  be  epigram  of  which  the 
point  is  pious  wish — which  has  been  so  often  recited  for  the 
purity  of  its  style,  a  purity  which  transcends  modern  printing. 
Perhaps  some  readers  may  think  that  Swift  cared  little  for  Whiston 
and  Ditton,  except  as  a  chance  hearing  of  their  plan  pointed  them 
out  as  good  marks.  But  it  was  not  so  :  the  clique  had  their  eye 
on  the  guilty  pair  before  the  publication  of  the  tract.  The  pre- 
face is  dated  July  7 ;  and  ten  days  afterwards  Arbuthnot  writes 
as  follows  to  Swift : — 

Whiston  has  at  last  published  his  project  of  the  longitude  ;  the  most 
ridiculous  thing  that  ever  was  thought  on.  But  a  pox  on  him  !  lie  has 
spoiled  one  of  my  papers  of  Scriblerus,  which  was  a  proposition  for  the 
longitude  not  very  unlike  his,  to  this  purpose  ;  that  since  there  was  no 
pole  for  east  and  west,  that  all  the  princes  of  Europe  should  join  and 
build  two  prodigious  poles,  upon  high  mountains,  with  a  vast  lighthouse 
to  serve  for  a  polestar.  I  was  thinking  of  a  calculation  of  the  time, 
charges,  and  dimensions.  Now  you  must  understand  his  project  is  by 
lighthouses,  and  explosion  of  bombs  at  a  certain  hour. 

The  plan  was  certainly  impracticable  ;  but  Whiston  and  Ditton 
might  have  retorted  that  they  were  nearer  to  the  longitude  than 
their  satirist  to  the  kingdom  of  heaven,  or  even  to  a  bishopric. 
Arbuthnot,  I  think,  here  and  elsewhere,  reveals  himself  as  the 
calculator  who  kept  Swift  right  in  his  proportions  in  the  matter 


80  A   BUDGET   OF  PARADOXES. 

of  the  Lilliputians,  Brobdingnagians,  &c.  Swift  was  very  ignorant 
about  things  connected  with  number.  He  writes  to  Stella  that 
he  has  discovered  that  leap-year  comes  every  four  years,  and  that 
all  his  life  he  had  thought  it  came  every  three  years.  Did  he 
begin  with  the  mistake  of  Caesar's  priests  ?  Whether  or  no,  when 
I  find  the  person  who  did  not  understand  leap-year  inventing 
satellites  of  Mars  in  correct  accordance  with  Kepler's  third  law, 
I  feel  sure  he  must  have  had  help. 


An  essay  concerning  the  late  apparition  in  the  heavens  on  the 
6th  of  March.  Proving  by  mathematical,  logical,  and  moral 
arguments,  that  it  cou'd  not  have  been  produced  meerly  by  the 
ordinary  course  of  nature,  but  must  of  necessity  be  a  prodigy. 
Humbly  offered  to  the  consideration  of  the  Royal  Society. 
London,  1716,  8vo. 

The  prodigy,  as  described,  was  what  we  should  call  a  very 
decided  and  unusual  aurora  borealis.  The  inference  was,  that 
men's  sins  were  bringing  on  the  end  of  the  world.  The  author 
thinks  that  if  one  of  the  old  '  threatening  prophets '  were  then 
alive,  he  would  give  '  something  like  the  following.'  I  quote  a 
few  sentences  of  the  notion  which  the  author  had  of  the  way  in 
which  Ezekiel,  for  instance,  would  have  addressed  his  Maker  in 
the  reign  of  George  the  First : — 

Begin  !  Begin  !  0  Sovereign,  for  once,  with  an  effectual  clap  of 
thunder.  ...  0  Deity  !  either  thunder  to  us  no  more,  or  when  you 
thunder,  do  it  home,  and  strike  with  vengeance  to  the  mark.  .  .  .  'Tis 
not  enough  to  raise  a  storm,  unless  you  follow  it  with  a  blow,  and  the 
thunder  without  the  bolt,  signifies  just  nothing  at  all.  .  .  .  Are  then 
your  lightnings  of  so  short  a  sight,  that  they  don't  know  how  to  hit, 
unless  a  mountain  stands  like  a  barrier  in  their  way  ?  Or  perhaps  so 
many  eyes  open  in  the  firmament  make  you  lose  your  aim  when  you 
shoot  the  arrow  ?  Is  it  this  ?  No  !  but,  my  dear  Lord,  it  is  your 
custom  never  to  take  hold  of  your  arms  till  you  have  first  bound  round 
your  majestic  countenance  with  gathered  mists  and  clouds. 

The  principles  of  the  Philosophy  of  the  Expansive  and  Con- 
tractive Forces.  ...  By  Robert  Greene,  M.A.,  Fellow  of  Clare 
Hall.  Cambridge,  1727,  folio. 

Sanderson  writes  to  Jones :  'The  gentleman  has  been  reputed 
mad  for  these  two  years  last  past,  but  never  gave  the  world  such 
ample  testimony  of  it  before.'  This  was  said  of  a  former  work  of 
Greene's,  on  solid  geometry,  published  in  1712,  in  which  he  gives 


NEWTON'S   APPLE.  81 

a  quadrature.  He  gives  the  same  or  another,  I  do  not  know 
which,  in  the  present  work,  in  which  the  circle  is  3^-  diameters. 
This  volume  is  of  981  good  folio  pages,  and  treats  of  all  thino-s, 
mental  and  material.  The  author  is  not  at  all  mad,  only  wrong 
on  many  points.  It  is  the  weakness  of  the  orthodox  follower  of 
any  received  system  to  impute  insanity  to  the  solitary  dissentient  : 
which  is  voted  (in  due  time)  a  very  wrong  opinion  about  Coper- 
nicus, Columbus,  or  Galileo,  but  quite  right  about  Robert  Greene. 
If  misconceptions,  acted  on  by  too  much  self-opinion,  b$  sufficient 
evidence  of  madness,  it  would  be  a  curious  inquiry  what  is  the 
least  per-centage  of  the  reigning  school  which  has  been  insane  at 
any  one  time.  Greene  is  one  of  the  sources  for  Newton  being  led 
to  think  of  gravitation  by  the  fall  of  an  apple  :  his  authorit"7  is 
the  gossip  of  Martin  Folkes.  Probably  Folkes  had  it  from 
Newton's  niece,  Mrs.  Conduitt,  whom  Voltaire  acknowledges  as 
//'">•  authority.  It  is  in  the  draft  found  among  Conduitt's  papers 
of  memoranda  to  be  sent  to  Fontenelle.  But  Fontenelle,  though 
a  great  retailer  of  anecdote,  does  not  mention  it  in  his  eloge  of 
Newton  ;  whence  it  may  be  suspected  that  it  was  left  out  in  the 
copy  forwarded  to  France.  D'Israeli  has  got  an  improvement  on 
the  story  :  the  apple  *  struck  him  a  smart  blow  on  the  head  : '  no 
doubt  taking  him  just  on  the  organ  of  causality.  He  was '  surprised 
at  the  force  of  the  stroke '  from  so  small  an  apple  :  but  then  the 
apple  had  a  mission  ;  Homer  would  have  said  it  was  Minerva  in 
the  form  of  an  apple.  '  This  led  him  to  consider  the  accelerating 
motion  of  falling  bodies,'  which  Galileo  had  settled  long  before  : 
'  from  whence  he  deduced  the  principle  of  gravity,'  which  many 
had  considered  before  him,  but  no  one  had  deduced  anything  from 
it.  I  cannot  imagine  whence  D'Israeli  got  the  rap  on  the  head, 
I  mean  got  it  for  Newton  :  this  is  very  unlike  his  usual  accounts 
of  things.  The  story  is  pleasant  and  possible  :  its  only  defect  is 
that  various  writings,  well  known  to  Newton,  a  very  learned 
mathematician,  had  given  more  suggestion  than  a  whole  sack  of 
apples  could  have  done,  if  they  had  tumbled  on  that  mighty  head 
all  at  once.  And  Pemberton,  speaking  from  Newton  himself, 
says  nothing  more  than  that  the  idea  of  the  moon  being  retained 
by  the  same  force  which  causes  the  fall  of  bodies  struck  him  for 
the  first  time  while  meditating  in  a  garden.  One  particular  tree 
at.  Woolsthorpe  has  been  selected  as  the  gallows  of  the  apple- 
shaped  goddess:  it  died  in  1820,  and  Mr.  Tumor  kept  the  wood  ; 
but  Sir  D.  Brewster  brought  away  a  bit  of  root  in  1814,  and  must 
have  had  it  on  his  conscience  for  43  years  that  he  may  have  killed 
the  tree.  Kepler's  suggestion  of  gravitation  with  the  inverse 

G 


82  A  BUDGET   QF   PARADOXES. 

distance,  and  Bouillaud's  proposed  substitution  of  the  inverse 
square  of  the  distance,  are  things  which  Newton  knew  better  than 
his  modern  readers.  I  discovered  two  anagrams  on  his  name, 
which  are  quite  conclusive  :  the  notion  of  gravitation  was  not 
new ;  but  Newton  vuent  on.  Some  wandering  spirit,  probably, 
whose  business  it  was  to  resent  any  liberty  taken  with  Newton's 
name,  put  into  the  head  of  a  friend  of  mine  eighty-one  anagrams 
on  my  own  pair,  some  of  which  hit  harder  than  any  apple. 

This  friend,  whom  I  must  not  name,  has  since  made  it  up  to 
about  800  anagrams  on  my  name,  of  which  I  have  seen  about 
650.  Two  of  them  I  have  joined  in  the  title-page  :  the  reader 
may  find  the  sense.  A  few  of  the  others  are  personal  remarks. 

Great  gun  !  do  us  a  sum  ! 
is  a  sneer  at  my  pursuits :  but, 

Go  !  great  sum  !  fau  du 

is  more  dignified. 

Sunt  agro  !  gaudemus, 

is  happy  as  applied  to  one  of  whom  it  may  be  said  : 

Ne'er  out  of  town  ;  'tis  such  a  horrid  life  : 
But  duly  sends  his  family  and  wife. 

Adsum,  nugator,  suge ! 

is  addressed  to  a  student  who  continues  talking  after  the  lecture 
has  commenced  :  oh  !  the  rascal ! 

Graduatus  sum !  nego 
applies  to  one  who  declined  to  subscribe  for  an  M.A.  degree. 

Usage  mounts  guard 
symbolises  a  person  of  very  fixed  habits. 

Gus  !     Gus  !  a  mature  don  ! 

August  man  !  sure,  god  ! 
And  Gus  must  argue,  0  ! 

Snug  as  mud  to  argue, 
Must  argue  on  gauds. 

A  mad  rogue  stung  us. 
Gag  a  numerous  stud. 

Go  !  turn  us  !  damage  us  ! 
Tug  us  !     O  drag  us  !     Amen. 

Grudge  us  !  moan  at  us  ! 
Daunt  us  !  gag  us  more  ! 

TJog-ear  us,  man  !  gut  us  ! 
D —  us  !  a  ro^ue  tuers  ! 


TREATISE   ASCRIBED   TO   NEWTON.  83 

are  addressed  to  me  by  the  circle-squarers  ;  and, 
O  !  Gus  !  tug  a  mean  surd  ! 

is  smart  upon  my  preference  of  an  incommensurable  value  of  TT 
to  3^,  or  some  such  simple  substitute.     While, 
Gus  !  Gus  !  at  'em  a'  round  ! 

ought  to  be  the  backing  of  the  scientific  world  to  the  author  of 
the  c  Budget  of  Paradoxes.' 

The  whole  collection  commenced  existence  in  the  head  of  a 
powerful  mathematician  during  some  sleepless  nights.  Seeing 
how  large  a  number  was  practicable,  he  amused  himself  by  in- 
venting a  digested  plan  of  finding  more. 

Is  there  any  one  whose  name  cannot  be  twisted  into  either 
praise  or  satire  ?  I  have  had  given  to  me, 

Thomas  Babington  Macaulay 
Mouths  big  :  a  Cantab  anomaly. 

A   treatise  of  the  system  of  the  world.     By  Sir  Isaac  Newton. 
Translated  into  English.     London,  1728,  8vo. 

I  think  I  have  a  right  to  one  little  paradox  of  my  own :  I 
greatly  doubt  that  Newton  wrote  this  book.  Castiglione,  in  his 
'Newtoni  Opuscula,'  gives  it  in  the  Latin  which  appeared  in  1731, 
not  for  the  first  time  ;  he  says  Angli  omnes  Newtono  trihuunt.  It 
appeared  just  after  Newton's  death,  without  the  name  of  any 
editor,  or  any  allusion  to  Newton's  recent  departure,  purporting 
to  be  that  popular  treatise  which  Newton,  at  the  beginning  of 
the  third  book  of  the  *  Principia,'  says  he  wrote,  intending  it  to 
be  the  third  book.  It  is  very  possible  that  some  observant  turn- 
penny might  construct  such  a  treatise  as  this  from  the  third  book, 
that  it  might  be  ready  for  publication  the  moment  Newton  could 
not  disown  it.  It  has  been  treated  with  singular  silence :  the 
name  of  the  editor  has  never  been  given.  Riband  mentions  it 
without  a  word  :  I  cannot  find  it  in  Brewster's  Newton,  nor  in  the 
'  Biographia  Britannica.'  There  is  no  copy  in  the  Catalogue  of 
the  Royal  Society's  Library,  either  in  English  or  Latin,  except  in 
Castiglione.  I  am  open  to  correction  ;  but  I  think  nothing  from 
Newton's  acknowledged  works  will  prove — as  laid  down  in  the 
suspected  work — that  he  took  Numa's  temple  of  Vesta,  with  a 
central  fire,  to  be  intended  to  symbolise  the  sun  as  the  centre  of 
our  system,  in  the  Copernican  sense. 

Mr.Edleston  gives  an  account  of  the  lectures  '  de  motu  corporum,* 
and  gives  the  corresponding  pages  of  the  Latin  '  De 

o  2 


84  A  BUDGET   OF   PAEADOXES. 

Mundi'  of  1731.  But  no  one  mentions  the  English  of  1728. 
This  English  seems  to  agree  with  the  Latin ;  but  there  is  a  mystery 
about  it.  The  preface  says,  '  That  this  work  as  here  published  is 
genuine  will  so  clearly  appear  by  the  intrinsic  marks  it  bears,  that 
it  will  be  but  losing  words  and  the  reader's  time  to  take  pains  in 
giving  him  any  other  satisfaction.'  Surely  fewer  words  would 
have  been  lost  if  the  prefator  had  said  at  once  that  the  work  was 
from  the  manuscript  preserved  at  Cambridge.  Perhaps  it  was  a 
mangled  copy  clandestinely  taken  and  interpolated. 

Lord  Bacon  not  the  author  of  'The  Christian  Paradoxes,'  being 
a  reprint  of  '  Memorials  of  Godliness  and  Christianity,'  by 
Herbert  Palmer,  B.D.  With  Introduction,  Memoir,  and  Notes, 
by  the  Rev.  Alexander  B.  Grosart,  Kenross.  (Private  circulation, 
1864). 

I  insert  the  above  in  this  place  on  account  of  a  slight  con- 
nexion with  the  last.  Bacon's  Paradoxes, — so  attributed — were 
first  published  as  his  in  some  asserted  '  Kemains,'  1648.  They 
were  admitted  into  his  works  in  1730,  and  remain  there  to  this 
day.  The  title  is  'The  Character  of  a  believing  Christian,  set 
forth  in  paradoxes  and  seeming  contradictions.'  The  following  is 
a  specimen : — 

He  believes  three  to  be  one  and  one  to  be  three  ;  a  father  not  to  be 
older  than  his  son ;  a  son  to  be  equal  with  his  father  ;  and  one  pro- 
ceeding from  both  to  be  equal  with  both  :  he  believes  three  persons  in 

one  nature,  and  two  natures  in  one  person He  believes  the  God 

of  all  grace  to  have  been  angry  with  one  that  never  offended  Him  ;  and 
that  God  that  hates  sin  to  be  reconciled  to  himself  though  sinning  con- 
tinually, and  never  making  or  being  able  to  make  Him  any  satisfaction. 
He  believes  a  most  just  God  to  have  punished  a  most  just  person,  and 
to  have  justified  himself,  though  a  most  ungodly  sinner.  He  believes 
himself  freely  pardoned,  and  yet  a  sufficient  satisfaction  was  made  for 
Mm. 

Who  can  doubt  that  if  Bacon  had  written  this,  it  must  have 
been  wrong?  Many  writers,  especially  on  the  Continent,  have 
taken  him  as  sneering  at  (Athanasian)  Christianity  right  and  left. 
Many  Englishmen  have  taken  him  to  be  quite  in  earnest,  and  to 
have  produced  a  body  of  edifying  doctrine.  More  than  a  century 
ago  the  Paradoxes  were  published  as  a  penny  tract ;  and,  again,  at 
the  same  price,  in  the  'Penny  Sunday  Eeader,'  vol.  vi.  No.  148,  a 
few  passages  were  omitted,  as  too  strong.  But  all  did  not  agree  : 
in  my  copy  of  Peter  Shaw's  edition  (vol.  ii.  p.  283)  the  Paradoxes 
have  been  cut  out  by  the  binder,  who  has  left  the  backs  of  the 
leaves.  I  never  had  the  curiosity  to  see  whether  other  copies  of 


BACON'S  PARADOXES.      SOCINIANS  AND  UNITARIANS.  85 

the  edition  have  been  served  in  the  same  way.  The  Keligious 
Tract  Society  republished  them  recently  in  '  Selections  from  the 
Writings  of  Lord  Bacon,'  (no  date;  bad  plan;  about  1863,  I 
suppose).  No  omissions  were  made,  so  far  as  I  find. 

I  never  believed  that  Bacon  wrote  this  paper  ;  it  has  neither  his 
sparkle  nor  his  idiom.  I  stated  my  doubts  even  before  I  heard 
that  Mr.  Spedding,  one  of  Bacon's  editors,  was  of  the  same  mind. 
(Athenceum,  July  16,  1864).  I  was  little  moved  by  the  wide  con- 
sent of  orthodox  men :  for  I  knew  how  Bacon,  Milton,  Newton, 
Locke,  &c.,  were  always  claimed  as  orthodox  until  almost  the 
present  day.  Of  this  there  is  a  remarkable  instance. 

Among  the  books  which  in  my  younger  day  were  in  some 
orthodox  publication  lists — I  think  in  the  list  of  the  Christian 
Knowledge  Society,  but  I  am  not  sure— was  Locke's  '  Eeason- 
ableness  of  Christianity.'  It  seems  to  have  come  down  from  the 
eighteenth  century,  when  the  battle  was  belief  in  Christ  against 
unbelief,  simplicite)^  as  the  logicians  say.  Now,  if  ever  there 
were  a  Socinian1  book  in  the  world,  it  is  this  work  of  Locke. 
'  These  two,'  says  Locke,  '  faith  and  repentance,  i.e.  believing 
Jesus  to  be  the  Messiah,  and  a  good  life,  are  the  indispensable 
conditions  of  the  new  covenant,  to  be  performed  by  all  those  who 
would  obtain  eternal  life.'  AIL  the  book  is  amplification  of  this 
doctrine.  Locke,  in  this  and  many  other  things,  followed  Hobbes, 
whose  doctrine,  in  the  Leviathan,  is  fidem,  quanta  ad  salutem 
necessaria  est,  contineri  in  hoc  articulo,  Jesus  est  Christus.  For 
this  Hobbes  was  called  an  atheist,  which  many  still  believe  him 
to  have  been :  some  of  his  contemporaries  called  him,  rightly, 

1  I  use  the  word  Socinian  because  it  was  so  much  used  in  Locke's  time ;  it  is  used 
in  our  own  day  by  the  small  fry,  the  unlearned  clergy  and  their  immediate  followers, 
as  a  term  of  reproach  for  all  Unitarians.  I  suspect  they  have  a  kind  of  liking  for  the 
word ;  it  sounds  like  so  sinful.  The  learned  clergy  and  the  higher  laity  know  better : 
they  know  that  the  bulk  of  the  modern  Unitarians  go  farther  than  Socinus,  and  are 
not  correctly  named  as  his  followers.  The  Unitarians  themselves  neither  desire  nor 
deserve  a  name  which  puts  them  one  point  nearer  to  orthodoxy  than  they  put 
themselves.  That  point  is  the  doctrine  that  direct  prayer  to  Jesus  Christ  is  lawful 
and  desirable  :  this  Socinus  held,  and  the  modern  Unitarians  do  not  hold.  Socinus, 
in  treating  the  subject  in  his  own  Insdtutio,  an  imperfect  catechism  which  he  left,  lays 
much  more  stress  on  John  xiv.  13  than  on  XT.  16  and  xvi.  23.  He  is  not  disinclined  to 
think  that  Patrem  should  be  in  the  first  citation,  where  some  put  it  ;  but  he  says 
that  to  ask  the  Father  in  the  name  of  the  Son  is  nothing  but  praying  to  the  Son  in 
prayer  to  the  Father.  He  labours  the  point  with  obvious  wish  to  secure  a  conclusive 
sanction.  In  the  Racovian  Catechism,  of  which  Faustus  Socinus  probably  drew  the 
first  sketch,  a  clearer  light  is  arrived  at.  The  translation  says  :  '  But  wherein  con- 
sists  the  divine  honour  due  to  Christ?  In  adoration  likewise  and  invocation.  For 
we  ought  at  all  times  to  adore  Christ,  and  may  in  our  necessities  address  our  pray*  ia 
to  him  as  often  as  we  please;  and  there  are  many  reasons  to  induce  us  to  do  this 
freely.'  There  are  some  who  like  accuracy,  even  in  aspersion. 


86  A  BUDGET   OF  PARADOXES. 

a  Socinian.  Locke  was  known  for  a  Socinian  as  soon  as  his  work 
appeared  :  Dr.  John  Edwards,  his  assailant,  says  he  is  '  Socin- 
ianized  all  over.'  Locke,  in  his  reply,  says  'there  is  not  one 
word  of  Socinianism  in  it : '  and  he  was  right :  the  positive 
Socinian  doctrine  has  not  one  word  of  Socinianism  in  it;  So- 
cinianism consists  in  omissions.  Locke  and  Hobbes  did  not  dare 
deny  the  Trinity :  for  such  a  thing  Hobbes  might  have  been 
roasted,  and  Locke  might  have  been  strangled.  Accordingly,  the 
well  known  way  of  teaching  Unitarian  doctrine  was  the  collection 
of  the  asserted  essentials  of  Christianity,  without  naming  the 
Trinity,  &c.  This  is  the  plan  Newton  followed,  in  the  papers  which 
have  at  last  been  published. 

So  I,  for  one,  thought  little  about  the  general  tendency  of 
orthodox  writers  to  claim  Bacon  by  means  of  the  Paradoxes.  I 
knew  that,  in  his  '  Confession  of  Faith  '  he  is  a  Trinitarian  of  a 
heterodox  stamp.  His  second  Person  takes  human  nature  before 
he  took  flesh,  not  for  redemption,  but  as  a  condition  precedent  of 
creation.  '  God  is  so  holy,  pure,  and  jealous,  that  it  is  impossible 
for  him  to  be  pleased  in  any  creature,  though  the  work  of  his 

own    hands [Genesis    i.    10,    12,    18,    21,  25,    31,    freely 

rendered].  But — purposing  to  become  a  Creator,  and  to  commu- 
nicate to  his  creatures,  he  ordained  in  his  eternal  counsel  that 
one  person  of  the  Godhead  should  be  united  to  one  nature,  and 
to  one  particular  of  his  creatures  ;  that  so,  in  the  person  of 
the  Mediator,  the  true  ladder  might  be  fixed,  whereby  God 
might  descend  to  his  creatures  and  his  creatures  might  ascend 
to  God ' 

This  is  republished  by  the  Eeligious  Tract  Society,  and  seems 
to  suit  their  theology,  for  they  confess  to  having  omitted  some 
things  of  which  they  disapprove. 

In  1864,  Mr.  Grosart  published  his  discovery  that  the  Paradoxes 
are  by  Herbert  Palmer ;  that  they  were  first  published  surrep- 
titiously, and  immediately  afterwards  by  himself,  both  in  1645 ; 
that  the  *  Eemains '  of  Bacon  did  not  appear  until  1 648 ;  that 
from  1645  to  1708,  thirteen  editions  of  the  'Memorials'  were 
published,  all  containing  the  Paradoxes.  In  spite  of  this,  the 
Paradoxes  were  introduced  into  Bacon's  works  in  1730,  where  they 
have  remained. 

Herbert  Palmer  was  of  good  descent,  and  educated  as  a  Puri- 
tan. He  was  an  accomplished  man,  one  of  the  few  of  his  day  who 
could  speak  French  as  well  as  English.  He  went  into  the  Church, 
and  was  beneficed  by  Laud,  in  spite  of  his  puritanism  ;  he  sat  in 
the  Assembly  of  Divines,  and  was  finally  President  of  Queens' 


CIRCLE  SQUARERS.      WHISTON   ON  THE  LONGITUDE.  87 

College,  Cambridge,  in  which  post  he  died,  August  13, 1647,  in  the 
46th  year  of  his  age. 

Mr.  Grosart  says,  speaking  of  Bacon's  '  Eemains,'  '  All  who  have 
had  occasion  to  examine  our  early  literature  are  aware  that  it  was 
a  common  trick  to  issue  imperfect,  false,  and  unauthorised  writings 
under  any  recently  deceased  .name  that  might  be  expected  to  take. 
The  Puritans,  down  to  John  Bunyan,  were  perpetually  expos- 
tulating and  protesting  against  such  procedure.'  I  have  met  with 
instances  of  all  this ;  but  I  did  not  know  that  there  was  so  much 
of  it :  a  good  collection  would  be  very  useful.  The  work  of  1728, 
attributed  to  Newton,  is  likely  enough  to  be  one  of  the  class. 

Demonstration  de  1'immobilitez  de  la  Terre.  .  .  .  Par  M.  de  la 
Jonehere,  Ingenieur  Fran9ais.  Londres,  1728,  8vo. 

A  synopsis  which  is  of  a  line  of  argument  belonging  to  the 
beginning  of  the  preceding  century. 

The  Circle  squared;  together  with  the  Ellipsis  and  several  re- 
flections on  it.  The  finding  two  geometrical  mean  proportionals, 

or  doubling  the  cube  geometrically.     By  Richard  Locke 

London,  no  date,  probably  about  1730,  8vo. 

According  to  Mr.  Locke,  the  circumference  is  three  diameters, 
three-fourths  the  difference  of  the  diameter  and  the  side  of  the 
inscribed  equilateral  triangle,  and  three- fourths  the  difference 
between  seven-eighths  of  the  diameter  and  the  side  of  the  same 
triangle.  This  gives,  he  says,  3-18897.  There  is  an  addition  to 
this  tract,  being  an  appendix  to  a  book  on  the  longitude. 

The  Circle  squar'd.  By  Thos.  Baxter,  Crathorn,  Cleaveland, 
Yorkshire.  London,  1732,  8vo. 

Here  TT  =  3-0625.     No  proof  is  offered. 

The  longitude  discovered  by  the  Eclipses,  Occultations,  and  Con- 
junctions of  Jupiter's  planets.  By  William  Whiston.  London, 
1738. 

This  tract  has,  in  some  copies,  the  celebrated  preface  contain- 
ing the  account  of  Newton's  appearance  before  the  Parliamentary 
Committee  on  the  longitude  question,  in  1714  (Brewster,  ii.  257- 
266).  This  *  historical  preface,'  is  an  insertion,  and  is  dated  April 
28,  1741,  with  four  additional  pages  dated  August  10, 1741.  The 
short  '  preface '  is  by  the  publisher,  John  Whiston,  the  author's 
son. 


88  A  BUDGET   OF  PAEADOXES. 


A- description  and  draught,  of  a  new-invented  machine  for  carrying 
vessels  or  ships  out  of,  or  into  any  harbour,  port,  or  river, 
against  wind  and  ti  le,  or  in  a  calm.  For  which,  His  Majesty 
has  granted  letters  patent,  for  the  sole  benefit  of  the  author,  for 
the  space  of  fourteen  years.  By  Jonathan  Hulls.  London  : 
printed  for  the  author,  1737.  Price  sixpence  (folding  plate  and 
pp.  48,  beginning  from  title). 

(I  ought  to  have  entered  this  tract  in  its  place.  It  is  so  rare 
that  its  existence  was  once  doubted.  It  is  the  earliest  description 
of  steam-power  applied  to  navigation.  The  plate  shows  a  barge, 
with  smoking  funnel,  and  paddles  at  the  stem,  towing  a  ship  of 
war.  The  engine,  as  described,  is  Newcomen's. 

In  1855,  John  Sheepshanks,  so  well  known  as  a  friend  of  Art 
and  a  public  donor,  reprinted  this  tract,  in  fac-simile,  from  his  own 
copy;  twenty-seven  copies  of  the  original  12mo.  size,  and  twelve 
on  old  paper,  small  4to.  I  have  an  original  copy,  wanting  the 
plate,  and  with  '  Price  sixpence '  carefully  erased,  to  the  honour  of 
the  book. 

It  is  not  known  whether  Hulls  actually  constructed  a  boat.  In 
all  probability  his  tract  suggested  to  Symington,  as  Symington  did 
to  Fulton.) 

Le  vrai  systeme  de  physique  generale  de  M.  Isaac  Newton  ex- 
pose et  analyse  en  parallele  avec  celui  de  Descartes.  By 
Louis  Castel  [Jesuit  and  F.R.S.].  Paris,  1743,  4to. 

This  is  an  elaborate  correction  of  Newton's  followers,  and  of 
Newton  himself,  who  it  seems  did  not  give  his  own  views  with 
perfect  fidelity.  Father  Castel,  for  instance,  assures  us  that  New- 
ton placed  the  sun  at  rest  in  the  centre  of  the  system.  Newton  left 
the  sun  to  arrange  that  matter  with  the  planets  and  the  rest  of  the 
universe.  In  this  volume  of  500  pages  there  is  right  and  wrong, 
both  clever. 

A  dissertation  on  the  ^Ether  of  Sir  Isaac  Newton.  By  Bryan 
Robinson,  M.D.  Dublin,  1743,.  8 vo. 

A  mathematical  work,  professing  to  prove  that  the  assumed 
ether  causes  gravitation. 

Mathematical  principles  of  theology,  or  the  existence  of  God 
geometrically  demonstrated.  By  Richard  Jack,  teacher  of 
Mathematics.  London,  1747,  8vo. 

Propositions  arranged  after  the  manner  of  Euclid,  with  beings 
represented  jay  circles  and  squares.  But  these  circles  and  squares 


JOHN  BERNOULLI  AND  DE  FAURE.  89 

are  logical  symbols,  not  geometrical  ones.  I  brought  this  book 
forward  to  the  Eoyal  Commission  on  the  British  Museum  as  an 
instance  of  the  absurdity  of  attempting  a  classed  catalogue  from 
the  titles  of  books.  The  title  of  this  book  sends  it  either  to  theo- 
logy or  geometry :  when,  in  fact,  it  is  a  logical  vagary.  Some  of 
the  houses  which  Jack  built  were  destroyed  by  the  fortune  of  war 
in  1745,  at  Edinburgh  :  who  will  say  the  rebels  did  no  good  what- 
ever ?  I  suspect  that  Jack  copied  the  ideas  of  J.  B.  Morinus, 
'  Quod  Deus  sit,'  Paris,  1636,  4to.,  containing  an  attempt  of  the 
same  kind,  but  not  stultified  with  diagrams. 

Dissertation,  decouverte,  et  demonstrations  de  la  quadrature 
mathematique  du  cercle.  Par  M.  de  Faure,  geometre.  [.<?.  I., 
probably  Geneva]  1747,  8vo. 

Analyse  de  la  Quadrature  du  Cercle.  Par  M.  de  Faure, 
Gentilhomme  Snisse.  Hague,  1749,  4to. 

According  to  this  octavo  geometer  and  quarto  gentleman,  a 
diameter  of  81  gives  a  circumference  of  256.  There  is  an  amusing 
circumstance  about  the  quarto  which  has  been  overlooked,  if 
indeed  the  book  has  ever  been  examined.  John  Bernoulli  (the 
one  of  the  day)  and  Koenig  have  both  given  an  attestation  :  my 
mathematical  readers  may  stare  as  they  please,  such  is  the  fact. 
But,  on  examination,  there  will  be  reason  to  think  the  two  sly 
Swiss  played  their  countryman  the  same  trick  as  the  medical  man 
played  Miss  Pickle,  in  the  novel  of  that  name.  The  lady  only 
wanted  to  get  his  authority  against  sousing  her  little  nephew,  and 
said,  '  Pray,  doctor,  is  it  not  both  dangerous  and  cruel  to  be  the 
means  of  letting  a  poor  tender  infant  perish  by  sousing  it  in  water 
as  cold  as  ice  ? ' — '  Downright  murder,  I  affirm,'  said  the  doctor  ; 
and  certified  accordingly.  De  Faure  had  built  a  tremendous 
scaffolding  of  equations,  quite  out  of  place,  and  feeling  cock-sure 
that  his  solutions,  if  correct,  would  square  the  circle,  applied  to 
Bernoulli  and  Koenig — who  after  his  tract  of  two  years  before, 
must  have  known  what  he  was  at — for  their  approbation  of  the 
solutions.  And  he  got  it,  as  follows,  well  guarded  : — 

Suivant  les  suppositions  posees  dans  ce  Memoire,  il  est  si  evident 
que  t  doit  etre  =  84,  y  =  1,  et  z  =  1,  que  cela  n'a  besoin  ni  de  preuve 
ni  d'autorite  pour  etre  reconnu  par  tout  le  monde. 

a  Basle  le  7e  Mai  1749.  JEAN  BERNOULLI. 

Je  souscris  au  jugement  de  Mr.  Bernoulli,  en  consequence  de  ces 
suppositions. 

a  la  Haye  le  21  Juin  17  I'.'.  S.  KOEXIG. 

On  which  de  Faure  remarks  with  triumph — as  I  have  no  doubt 


90  .         A  BUDGET   OF  PARADOXES. 

it  was  intended  he  should  do — '  il  conste  clairement  par  ma 
presente  Analyse  et  Demonstration,  qu'ils  y  ont  deja  reconnu  et 
approuve  parfaitement  que  la  quadrature  du  cercle  est  mathema- 
tiquement  demontree.'  It  should  seem  that  it  is  easier  to  square 
the  circle  than  to  get  round  a  mathematician. 

An  attempt  to  demonstrate  that  all  the  Phenomena  in  Nature 
may  be  explained  by  two  simple  active  principles,  Attraction 
and  Repulsion,  wherein  the  attractions  of  Cohesion,  Gravity 
and  Magnetism  are  shown  to  be  one  and  the  same.  By  Go  win 
Knight.  London,  1748,  4to. 

Dr.  Knight  was  Mr.  Panizzi's  archetype,  the  first  Principal 
Librarian  of  the  British  Museum.  He  was  celebrated  for  his 
magnetical  experiments.  This  work  was  long  neglected  ;  but  is 
now  recognised  as  of  remarkable  resemblance  to  modern  specula- 
tions. 

An  original  theory  or  Hypothesis  of  the  Universe.  By  Thomas 
Wright  of  Durham.  London,  4to.  1750. 

Wright  is  a  speculator  whose  thoughts  are  now  part  of  our 
current  astronomy.  He  took  that  view — or  most  of  it — of  the 
milky  way  which  afterwards  suggested  itself  to  William  Herschel. 
I  have  given  an  account  of  him  and  his  work  in  the  Philosophi- 
cal Magazine  for  April,  1848. 

Wright  was  mathematical  instrument  maker  to  the  King ;  and 
kept  a  shop  in  Fleet  Street.  Is  the  celebrated  business  of  Trough- 
ton  &  Simms,  also  in  Fleet  Street,  a  lineal  descendant  of  that  of 
Wright  ?  It  is  likely  enough,  more  likely  than  that — as  I  find 
him  reported  to  have  affirmed — Prester  John  was  the  descendant 
of  Solomon  and  the  Queen  of  Sheba.  Having  settled  it  thus,  it 
struck  me  that  I  might  apply  to  Mr.  Simms,  and  he  informs  me 
that  it  is  as  I  thought,  the  line  of  descent  being  Wright,  Cole, 
John  Troughton,  Edward  Troughton,  Troughton  &  Simms. 

The  theology  and  philosophy  in  Cicero's  Somnium  Scipionis 
explained.  Or,  a  brief  attempt  to  demonstrate,  that  the 
Newtonian  system  is  perfectly  agreeable  to  the  notions  of  the 
wisest  ancients  :  and  that  mathematical  principles  are  the  only 
sure  ones.  [By  Bishop  Home,  at  the  age  of  nineteen.] 
London,  1751,  8vo. 

This  tract,  which  was  not  printed  in  the  collected  works,  and  is 
now  excessively  rare,  is  mentioned  in  Notes  and  Queries,  1st  S., 


BISHOP  HORNE  AND   OLD  BEN  MARTIN.  91 

v.  490,  573  ;  2nd  S.,  ix.  15.  The  boyish  satire  on  Newton  is 
amusing.  Speaking  of  old  Benjamin  Martin,  he  goes  on  as 
follows : — 

But  the  most  elegant  account  of  the  matter  [attraction]  is  by  that 
hominiform  animal,  Mr.  Benjamin  Martin,  who  having  attended 
Dr.  Desaguliers'  fine,  raree,  gallanty  shew  for  some  years  [Desa- 
guliers  was  one  of  the  first  who  gave  public  experimental  lectures, 
before  the  saucy  boy  was  born]  in  the  capacity  of  a  turnspit,  has,  it 
seems,  taken  it  into  his  head  to  set  up  for  a  philosopher. 

Thus  is  preserved  the  fact,  unknown  to  his  biographers,  that 
Benj.  Martin  was  an  assistant  to  Desaguliers  in  his  lectures. 
Hutton  says  of  him,  that  '  he  was  well  skilled  in  the  whole  circle 
of  the  mathematical  and  philosophical  sciences,  and  wrote  useful 
books  on  every  one  of  them' :  this  is  quite  true  ;  and  even  at  this 
day  he  is  read  by  twenty  where  Home  is  read  by  one  ;  see  the 
stalls,  passim,.  All  that  I  say  of  him,  indeed  my  knowledge  of 
the  tract,  is  due  to  this  contemptuous  mention  of  a  more  durable 
man  than  himself.  My  assistant  secretary  at  the  AstronomicaJ 
Society,  the  late  Mr.  Epps,  bought  the  copy  at  a  stall  because  his 
eye  was  caught  by  the  notice  of  '  Old  Ben  Martin,'  of  whom  he 
was  a  great  reader.  Old  Ben  could  not  be  a  Fellow  of  the  Royal 
Society,  because  he  kept  a  shop :  even  though  the  shop  sold 
nothing  but  philosophical  instruments.  Thomas  Wright,  similarly 
situated  as  to  shop  and  goods,  never  was  a  Fellow.  The  Society 
of  our  day  bas  greatly  degenerated  :  those  of  the  old  time  would 
be  pleased,  no  doubt,  that  the  glories  of  their  day  should  be 
commemorated.  In  the  early  days  of  the  Society,  there  was  a 
similar  difficulty  about  Graunt,  the  author  of  the  celebrated  work 
on  mortality.  But  their  royal  patron,  'who  never  said  a  foolish 
thing,'  sent  them  a  sharp  message,  and  charged  them  if  they 
found  any  more  such  tradesmen,  they  should  'elect  them  without 
more  ado.' 

Home's  first  pamphlet  was  published  when  he  was  but  twenty- 
one  years  old.  Two  years  afterwards,  being  then  a  Fellow  of  bis 
college,  and  having  seen  more  of  the  world,  he  seems  to  have  felt 
that  his  manner  was  a  little  too  pert.  He  endeavoured,  it  is  said, 
to  suppress  his  first  tract :  and  copies  are  certainly  of  extreme 
rarity.  He  published  the  following  as  his  maturer  view  : 


92  A  BUDGET  OF  PAEADOXES. 


A  fair,  candid,  and  impartial  state  of  the  case  between  Sir 
Isaac  Newton  and  Mr.  HutcLinson.  In  which  is  shown  how 
for  a  system  of  physics  is  capable  of  mathematical  demonstra- 
tion; how  far  Sir  Isaac's,  as  such  a  system,  has  that  demon- 
stration ;  and  consequently,  what  regard  Mr.  Hutchinson's  claim 
may  deserve  to  have  paid  to  it.  By  George  Home,  M.A. 
Oxford,  1753,  8vo. 

It  must  be  remembered  that  the  successors  of  Newton  were 
very  apt  to  declare  that  Newton  had  demonstrated  attraction  as  a 
physical  cause :  he  had  taken  reasonable  pains  to  show  that  he 
did  not  pretend  to  this.  If  any  one  had  said  to  Newton,  I  hold 
that  every  particle  of  matter  is  a  responsible  being  of  vast  intel- 
lect, ordered  by  the  Creator  to  move  as  it  would  do  if  every  other 
particle  attracted  it,  and  gifted  with  power  to  make  its  way  in 
true  accordance  with  that  law,  as  easily  as  a  lady  picks  her  way 
across  the  street ;  what  have  you  to  say  against  it  ? — Newton 
must  have  replied,  Sir !  if  you  really  undertake  to  maintain  this 
as  demonstrable,  your  soul  had  better  borrow  a  little  power  from 
the  particles  of  which  your  body  is  made :  if  you  merely  ask  me 
to  refute  it,  I  tell  you  that  I  neither  can  nor  need  do  it;  for 
whether  attraction  comes  in  this  way  or  in  any  other,  it  comes, 
and  that  is  all  I  have  to  do  with  it. 

The  reader  should  remember  that  the  word  attraction,  as  used 
by  Newton  and  the  best  of  his  followers,  only  meant  a  drawing 
towards,  without  any  implication  as  to  the  cause.  Thus  whether 
they  said  that  matter  attracts  matter,  or  that  young  lady  attracts 
young  gentleman,  they  were  using  one  word  in  one  sense.  Newton 
found  that  the  law  of  the  first  is  the  inverse  square  of  the  dis- 
tance :  I  am  not  aware  that  the  law  of  the  second  has  been 
discovered ;  if  there  be  any  chance,  we  shall  see  it  at  the  year 
1856  in  this  list. 

In  this  point  young  Home  made  a  hit.  He  justly  censures 
those  who  fixed  upon  Newton  a  more  positive  knowledge  of  what 
attraction  is  than  he  pretended  to  have.  'He  has  owned  over 
and  over  he  did  not  know  what  he  meant  by  it — it  might  be  this, 
or  it  might  be  that,  or  it  might  be  anything,  or  it  might  be 
nothing.'  With  the  exception  of  the  nothing  clause,  this  is  true, 
though  Newton  might  have  answered  Home  by  '  Thou  hast  said 
it,' 

(I,thought  everybody  knew  the  meaning  of  '  Thou  hast  said  it :' 
but  I  was  mistaken.  In  three  of  the  evangelists  2v  \systs  is  the 


HOKNE   ON   NEWTON.      WEYMAN   LEE.  93 

answer  to  '  Art  thou  a  king  ?'  The  force  of  this  answer,  as  always 
understood,  is  '  That  is  your  way  of  putting  it.'  The  Puritans, 
who  lived  in  Bible  phrases,  so  understood  it:  and  Walter  Scott, 
who  caught  all  peculiarities  of  language  with  great  effect,  makes 
a  marked  instance, '  Were  you  armed  ? —  I  was  not — I  went  in  my 
calling,  as  a  preacher  of  (rod's  word,  to  encourage  them  that  drew 
the  sword  in  His  cause.  In  other  words,  to  aid  and  abet  the 
rebels,  said  the  Duke.  Thou  hast  spoken  it,  replied  the  prisoner.') 

Again,  Home  quotes  Eowning  as  follows  :  — 

Mr.  Rowning,  pt.  2  p.  5  in  a  nobe,  has  a  very  pretty  conceit  upon 
this  same  subject -of  attraction,  about  every  particle  of  a  fluid  being1 
intrenched  in  three  spheres  of  attraction  and  repulsion,  one  within 
another,  '  the  innermost  of  which  (he  says)  is  a  sphere  of  repulsion, 
which  keeps  them  from  approaching  into  contact ;  the  next,  a  sphere 
of  attraction,  diffused  around  this  of  repulsion,  by  which  the  particles 
are  disposed  to  run  together  into  drops  ;  and  the  outermost  of  all,  a 
sphere  of  repulsion,  whereby  they  repel  each  other,  when  removed  out 
of  the  attraction.'  So  that  between  the  urginys,  and  suUicitations,  of 
one  and  t'other,  a  poor  unhappy  particle  must  ever  be  at  his  wit's  end, 
not  knowing  which  way  to  turn,  or  whom  to  obey  first. 

Rowning  has  here  started  the  notion  which  Boscovich  afterwards 
developed. 

I  may  add  to  what  precedes  that  it  cannot  be  settled  that,  as 
Granger  says,  Desaguliers  was  the  first  who  gave  experimental 
lectures  in  London.  William  Whiston  gave  some,  and  Francis 
Hauksbee  made  the  experiments.  The  prospectus,  as  we  should 
now  call  it,  is  extant,  a  quarto  tract  of  plates  and  descriptions, 
without  date.  Whiston,  in  his  life,  gives  1714  as  the  first  date 
of  publication,  and  therefore,  no  doubt,  of  the  lectures.  Desagu- 
liers removed  to  London  soon  after  1712,  and  commenced  his 
lectures  soon  after  that.  It  will  be  rather  a  nice  point  to  settle 
which  lectured  first;  probabilities  seem  to  go  in  favour  or 
Whiston. 

An  Essay  to  ascertain  the  value  of  leases,  and  annuities  for 
years  and  lives.  By  W[eyman]  L[ee].  London,  1737,  8vo. 

A  valuation  of  Annuities  and  Leases  certain,  for  a  single  life. 
By  Weyman  Lee,  Esq.  of  the  Inner  Temple.  London,  1751, 
8vo.  Third  edition,  177:!. 

Every  branch  of  exact  science  has  its  paradoxer.  The  world  at 
large  cannot  tell  with  certainty  who  is  right  in  such  questions  as 
squaring  the  circle,  &c.  Mr.  Weyrnan  Lee  was  the  assailant  of 


94  A   BUDGET   OF  PARADOXES. 

what  all  who  had  studied  called  demonstration  in  the  question  of 
annuities.  He  can  be  exposed  to  the  world :  for  his  error  arose 
out  of  his  not  being  able  to  see  that  the  whole  is  the  sum  of  all 
its  parts. 

By  an  annuity,  say  of  100£.,  now  bought,  is  meant  that  the 
buyer  is  to  have  for  his  money  lOQl.  in  a  year,  if  he  be  then 
alive,  100L  at  the  end  of  two  years,  if  then  alive,  and  so 
on.  It  is  clear  that  he  would  buy  a  life  annuity  if  he 
should  buy  the  first  100£.  in  one  office,  the  second  in  another, 
and  so  on.  All  the  difference  between  buying  the  whole  from 
one  office,  and  buying  all  the  separate  contingent  payments  at 
different  offices,  is  immaterial  to  calculation.  Mr.  Lee  would 
have  agreed  with  the  rest  of  the  world  about  the  payments  to  be 
made  to  the  several  different  offices,  in  consideration  of  their  several 
contracts  :  but  he  differed  from  every  one  else  about  the  sum  to 
be  paid  to  one,  office.  He  contended  that  the  way  to  value  an 
annuity  is  to  find  out  the  term  of  years  which  the  individual  has 
an  even  chance  of  surviving,  and  to  charge  for  the  life  annuity 
the  value  of  an  annuity  certain  for  that  term. 

It  is  very  common  to  say  that  Lee  took  the  average  life,  or  ex- 
pectation, as  it  is  wrongly  called,  for  his  term :  and  this  I  have 
done  myself,  taking  the  common  story.  Having  exposed  the 
absurdity  of  this  second  supposition,  taking  it  for  Lee's,  in  my 
'Formal  Logic,'  I  will  now  do  the  same  with  the  first. 

A  mathematical  truth  is  true  in  its  extreme  cases.  Lee's  prin- 
ciple is  that  an  annuity  on  a  life  is  the  annuity  made  certain  for 
the  term  within  which  it  is  an  even  chance  the  life  drops.  If, 
then,  of  a  thousand  persons,  500  be  sure  to  die  within  a  year,  and 
the  other  500  be  immortal,  Lee's  price  of  an  annuity  to  any  one 
of  these  persons  is  the  present  value  of  one  payment :  for  one  year 
is  the  term  which  each  one  has  an  even  chance  of  surviving  and 
not  surviving.  But  the  true  value  is  obviously  half  that  of  a 
perpetual  annuity :  so  that  at  5  per  cent.  Lee's  rule  would  give 
less  than  the  tenth  of  the  true  value.  It  must  be  said  for  the 
poor  circle-squarers,  that  they  never  err  so  much  as  this. 

Lee  would  have  said,  if  alive,  that  I  have  put  an  extreme  case  : 
but  any  universal  truth  is  true  in  its  extreme  cases.  It  is  not 
fair  to  bring  forward  an  extreme  case  against  a  person  who  is 
speaking  as  of  usual  occurrences  :  but  it  is  quite  fair  when,  as 
frequently  happens,  the  proposer  insists  upon  a  perfectly  general 
acceptance  of  his  assertion.  And  yet  many  who  go  the  whole  hog 
protest  against  being  tickled  with  the  tail.  Counsel  in  court  are 
good  instances:  they  are  paradoxers  by  trade.  June  13,  1849,  at 


MONTUCLA'S  HISTORY  OF  CIRCLE  SQUARING.  95 

Hertford,  there  was  an  action  about  a  ship,  insured  against  a  total 
loss  :  some  planks  were  saved,  and  the  underwriters  refused  to  pay. 
Mr.  Z.  (for  deft.)  'There  can  be  no  degrees  of  totality;  and  some 
timbers  were  saved.' — L.  C.  B.  'Then  if  the  vessel  were  burned  to 
the  water's  edge,  and  some  rope  saved  in  the  boat,  there  would  be 
no  total  loss.' — Mr.  Z.  'This  is  putting  a  very  extreme  case.' — 
L.  C.  B.  'The  argument  would  go  that  length.'  What  would 
Judge  Z. — as  he  now  is — say  to  the  extreme  case  beginning  some- 
where between  six  planks  and  a  bit  of  rope  ? 

Histoire  des  recherches  sur  la  quadrature  du  cercle.  .  .  .  avec 
une  addition  concernant  les  problemes  de  la  duplication  du 
cube  et  de  la  trisection  de  1'anglo.  Paris,  1754,  12mo.  [By 
Montucla.] 

This  is  the  history  of  the  subject.  It  was  a  little  episode  to 
the  great  history  of  mathematics  by  Montucla,  of  which  the  first 
edition  appeared  in  1758.  There  was  much  addition  at  the  end 
of  the  fourth  volume  of  the  second  edition ;  this  is  clearly  by 
Montucla,  though  the  bulk  of  the  volume  is  put  together,  with 
help  from  Montucla's  papers,  by  Lalande.  There  is  also  a  second 
edition  of  the  history  of  the  quadrature,  Paris,  1831,  8vo, 
edited,  I  think,  by  Lacroix ;  of  which  it  is  the  great  fault  that  it 
makes  hardly  any  use  of  the  additional  matter  just  mentioned.  • 

Montucla  is  an  admirable  historian  when  he  is  writing  from  his 
own  direct  knowledge :  it  is  a  sad  pity  that  he  did  not  tell  us 
when  he  was  depending  on  others.  We  are  not  to  trust  a  quarter 
of  his  book,  and  we  must  read  many  other  books  to  know  which 
quarter.  The  fault  is  common  enough,  but  Montucla's  good 
three-quarters  is  so  good  that  the  fault  is  greater  in  him  than  in 
most  others :  I  mean  the  fault  of  not  acknowledging  ;  for  an 
historian  cannot  read  everything.  But  it  must  be  said  that 
mankind  give  little  encouragement  to  candour  on  this  point. 
Hallam,  in  his  '  History  of  Literature,'  states  with  his  own  usual 
instinct  of  honesty  every  case  in  which  he  depends  upon  others  : 
Montucla  does  not.  And  what  is  the  consequence? — Montucla  is 
trusted,  and  believed  in,  and  cried  up  in  the  bulk  ;  while  the 
smallest  talker  can  lament  that  Hallam  should  be  so  unequal  and 
apt  to  depend  on  others,  without  remembering  to  mention  that 
Hallam  himself  gives  the  information.  As  to  a  universal  history 
of  any  great  subject  being  written  entirely  upon  primary  know- 
ledge, it  is  a  thing  of  which  the  possibility  is  not  yet  proved  by 
an  example.  Delambre  attempted  it  with  astronomy,  and  was 
removed  by  death  before  it  was  finished,  to  say  nothing  of  the 
gaps  he  left. 


96  A   BUDGET   OF   PARADOXES. 

Montucla  was  nothing  of  a  bibliographer,  and  his  descriptions 
of  books  in  the  first  edition  were  insufficient.  The  Abbe  Rive 
fell  foul  of  him,  and  as  the  phrase  is,  gave  it  him.  Montucla 
took  it  with  great  good  humour,  tried  to  mend,  and,  in  his  second 
edition,  wished  his  critic  had  lived  to  see  the  vernis  de  biblio- 
graphe  which  he  had  given  himself. 

I  have  seen  Montucla  set  down  as  an  esprit  fort,  more  than 
once  :  wrongly,  I  think.  When  he  mentions  Barrow's  address  to 
the  Almighty,  he  adds,  '  On  voit,  au  reste,  par  la,  que  Barrow 
etoit  un  pauvre  philosophe  ;  car  il  croyait  en  1'immortalite  de 
1'ame,  et  en  une  Divinite  autre  que  la  nature  universelle.'  This 
is  irony,  not  an  expression  of  opinion.  In  the  book  of  mathe- 
matical recreations  which  Montucla  constructed  upon  that  of 
Ozanam,  and  Ozanam  upon  that  of  Van  Etten,  now  best  known  in 
England  by  Mutton's  similar  treatment  of  Montucla,  there  is  an 
amusing  chapter  on  the  quadrators.  Montucla  refers  to  his  own 
anonymous  book  of  1754  as  a  curious  book  published  by  Jombert. 
He  seems  to  have  been  a  little  ashamed  of  writing  about  circle- 
squarers  :  what  a  slap  on  the  face  for  an  unborn  Budgeteer  I 

Montucla  says,  speaking  of  France,  that  he  finds  three  notions 
prevalent  among  the  cyclometers  :  1.  that  there  is  a  large  reward 
offered  for  success;  2.  that  the  longitude  problem  depends  on 
that  success  ;  3.  that  the  solution  is  the  great  end  and  object  of 
geometry.  The  same  three  notions  are  equally  prevalent  among 
the  same  class  in  England.  No  reward  has  ever  been  offered  by 
the  government  of  either  country.  The  longitude  problem  in 
no  way  depends  upon  perfect  solution  :  existing  approximations 
are  sufficient  to  a  point  of  accuracy  far  beyond  what  can  be 
wanted.  And  geometry,  content  with  what  exists,  has  long  passed 
on  to  other  matters.  Sometimes  a  cyclometer  persuades  a  skipper 
who  has  made  land  in  the  wrong  place  that  the  astronomers  are  in 
fault,  for  using  a  wrong  measure  of  the  circle ;  and  the  skipper 
thinks  it  a  very  comfortable  solution  S  And  this  is  the  utmost 
that  the  proble.ni  ever  has  to  do  with  longitude. 

Antinewtoniamsmus.      By     Cielestino     Cominale,     M.D.    Naples, 
1754  and  1756,  2  vols.  4to. 

The  first  volume  upsets  the  theory  of  light;  the  second 
vacuum,  vis  inertise,  gravitation,  and  attraction.  I  confess  I 
never  attempted  these  big  Latin  volumes,  numbering  450  closely- 
printed  quarto  pages.  The  man  who  slays  Newton  in  a  pamphlet 
is  the  man  for  me.  But  I  will  lend  them  to  anybody  who  will 


REWARD   FOR   QUADRATURE.  97 

give  security,  himself  in  500£.,  and  two  sureties  in  2501.  each,  that 
he  will  read  them  through,  and  give  a  full  abstract ;  and  I  will 
not  exact  security  for  their  return.  I  have  never  seen  any 
mention  of  this  book :  it  has  a  printer,  but  not  a  publisher,  as 
happens  with  so  many  unrecorded  books. 

1755.  The  French  Academy  of  Sciences  came  to  the  deter- 
mination not  to  examine  any  more  quadratures  or  kindred 
problems.  This  was  the  consequence,  no  doubt,  of  the  publication 
of  Montucla's  book  :  the  time  was  well  chosen  ;  for  that  book  was 
a  full  justification  of  the  resolution.  The  Eoyal  Society  followed 
the  same  course,  I  believe,  a  few  years  afterwards.  When  our 
Board  of  Longitude  was  in  existence,  most  of  its  time  was  con- 
sumed in  listening  to  schemes,  many  of  which  included  the 
quadrature  of  the  circle.  It  is  certain  that  many  quadrators  have 
imagined  the  longitude  problem  to  be  connected  with  theirs  :  and 
no  doubt  the  notion  of  a  reward  being  offered  by  Government  for 
a  true  quadrature  is  a  result  of  the  reward  offered  for  the  longi- 
tude. Let  it  also  be  noted  that  this  longitude  reward  was  not 
a  premium  upon  excogitation  of  a  mysterious  difficulty.  The 
legislature  was  made  to  know  that  the  rational  hopes  of  the 
problem  were  centred  in  the  improvement  of  the  lunar  tables  and 
the  improvement  of  chronometers.  To  these  objects  alone,  and 
by  name,  the  offer  was  directed :  several  persons  gained  rewards 
for  both ;  and  the  offer  was  finally  repealed. 

Fundamentals  Figura  Georaetrica,  primas  tantum  lineas  circuli 
quadrature  possibilitatis  ostendens.  By  Niels  Erichsen 
(Nicolaus  Ericius),  shipbuilder,  of  Copenhagen.  Copenhagen, 
1755,  12mo. 

This  was  a  gift  from  my  oldest  friend  who  was  not  a  relative, 
Dr.  Samuel  Maitland  of  the  '  Dark  Ages.'  He  found  it  among 
his  books,  and  could  not  imagine  how  he  came  by  it :  I  could 
have  told  him.  He  once  collected  interpretations  of  the  Apo- 
calypse :  and  auction  lots  of  such  books  often  contain  quadratures. 
The  wonder  is  he  never  found  more  than  one. 

The  quadrature  is  not  worth  notice.  Erichsen  is  the  only 
squarer  I  have  met  with  who  has  distinctly  asserted  the  particulars 
of  that  reward  which  has  been  so  frequently  thought  to  have  been 
offered  in  England.  He  says  that,  in  1747,  the  Eoyal  Society,  on 
the  2nd  of  June,  offered  to  give  a  large  reward  for  the  quadrature  of 
the  circle  and  a  true  explanation  of  magnetism,  in  addition  to 
30,000^.  previously  promised  for  the  same.  I  need  hardly  say  that 

ir 


98  A  BUDGET   OE  PARADOXES. 

the  Royal  Society  had  not  30,000£.  at  that  time,  and  would  not,  if 
it  had  had  such  a  sum,  have  spent  it  on  the  circle,  nor  on  magnetic 
theory  ;  nor  would  it  have  coupled  the  two  things.  On  this  book, 
see  Notes  and  Queries,  1st  S.  xii.  306.  Perhaps  Erichsen  meant 
that  the  30,000£.  had  been  promised  by  the  Government,  and  the 
addition  by  the  Eoyal  Society. 

October  8,  1866.  I  receive  a  letter  from  a  cyclometer  who 
understands  that  a  reward  is  offered  to  any  one  who  will  square 
the  circle,  and  that  all  competitors  are  to  send  their  plans  to  me. 
The  hoaxers  have  not  yet  failed  out  of  the  land. 

Theoria  Philosophise  Naturalis  redacta  ad  unicam  legem  virium 
in  natura  existentium.  Editio  Veneta  prima.  By  Roger  Joseph 
Boscovich.  Venice,  1763,  4to. 

The  first  edition  is  said  to  be  of  Vienna,  1758.  This  is  a 
celebrated  work  on  the  molecular  theory  of  matter,  grounded  on 
the  hypothesis  of  spheres  of  alternate  attraction  and  repulsion. 
Boscovich  was  a  Jesuit  of  varied  pursuit.  During  his  measure- 
ment of  a  degree  of  the  meridian,  while  on  horseback  or  waiting 
for  his  observations,  he  composed  a  Latin  poem  of  about  five 
thousand  verses  on  eclipses,  with  notes,  which  he  dedicated  to  the 
Eoyal  Society  :  '  De  Solis  et  Lunse  defectibus,'  London,  Millar 
and  Dodsley,  1760,  4to. 

Traite  de  paix  entre  DCS  Cartes  et  Newton,  precede  des  vies 
littcraires  de  ces  deux  chefs  de  la  physique  moderne.  .  .  .  By 
Aime  Henri  Paulian.  Avignon,  1763,  12mo. 

I  have  had  these  books  for  many  a  year  without  feeling  the 
least  desire  to  see  how  a  lettered  Jesuit  would  atone  Descartes 
and  Newton.  On  looking  at  my  two  volumes,  I  find  that  one 
contains  nothing  but  the  literary  life  of  Des  Cartes  ;  the  other 
nothing  but  the  literary  life  of  Newton.  The  preface  indicates 
more  :  and  Watt  mentions  three  volumes.  I  dare  say  the  first 
two  contain  all  that  is  valuable.  On  looking  more  attentively  at 
the  two  volumes,  I  find  them  both  readable  and  instructive ;  the 
account  of  Newton  is  far  above  that  of  Voltaire,  but  not  so 
popular.  But  he  should  not  have  said  that  Newton's  family 
came  from  Newton  in  Ireland.  Sir  Rowland  Hill  gives  fourteen 
Newtons  in  Ireland :  twice  the  number  of  the  cities  that  con- 
tended for  the  birth  of  Homer  may  now  contend  for  the  origin  of 
Newton,  on  the  word  of  Father  Paulian. 


BAILLY'S  LETTERS  TO  VOLTAIRE.  99 


Philosophical  Essays,  in  three  parts.  By  B.  Lovett,  Lay 
Clerk  of  the  Cathedral  Church  of  Worcester.  Worcester,  1766, 
8vo. 

The  Electrical  Philosopher:  containing  a  new  system  of 
physics  founded  upon  the  principle  of  an  universal  Plenum 
of  elementary  fire  .  .  .  By  R.  Lovett.  Worcester,  1774,  8vo. 

Mr.  Lovett  was  one  of  those  ether  philosophers  who  bring  in 
elastic  fluid  as  an  explanation  by  imposition  of  words,  without 
deducing  any  one  phenomenon  from  what  we  know  of  it.  And 
yet  he  says  that  attraction  has  received  no  support  from  geome- 
try ;  though  geometry,  applied  to  a  particular  law  of  attraction, 
had  shown  how  to  predict  the  motions  of  the  bodies  of  the  t^olar 
system.  He,  and  many  of  his  stamp,  have  not  the  least  idea  of 
the  confirmation  of  a  theory  by  accordance  of  deduced  results 
with  observation  posterior  to  the  theory. 

Lettres  sur  1'Atlantide  de  Platon,  et  sur  1'ancien  Histoire  de 
1' Asie,  pour  servir  de  suite  aux  lettres  sur  1'origine  des  Sciences, 
adressees  a  M.  de  Voltaire,  par  M.  Bailly.  London  and  Paris, 
'1779,  8vo. 

I  might  enter  here  all  Bailly's  histories  of  astronomy.  The 
paradox  which  runs  through  them  all  more  or  less,  is  the  doctrine 
that  astronomy  is  of  immense  antiquity,  coming  from  some 
forgotten  source,  probably  the  drowned  island  of  Plato,  peopled 
by  a  race  whom  Bailly  makes,  as  has  been  said,  to  teach  us 
everything  except  their  existence  and  their  name.  These  books, 
the  first  scientific  histories  which  belong  to  readable  literature, 
made  a  great  impression  by  power  of  style  :  Delambre  created  a 
strong  reaction,  of  injurious  amount,  in  favour  of  history  founded 
on  contemporary  documents,  which  early  astronomy  cannot 
furnish.  These  letters  are  addressed  to  Voltaire,  and  continue 
the  discussion.  There  is  one  letter  of  Voltaire,  being  the  fourth, 
dated  Feb.  27,  1777,  and  signed  '  le  vieux  malade  de  Ferney,  V. 
puer  centum  annorum.'  Then  begin  Bailly's  letters,  from 
January  16  to  May  12,  1778.  From  some  ambiguous  expressions 
in  the  Preface,  it  would  seem  that  these  are  fictitious  letters,  sup- 
posed to  be  addressed  to  Voltaire  at  their  dates.  Voltaire  went 
to  Paris  February  10,  1778,  and  died  there  May  30.  Nearly  all 
this  interval  was  his  closing  scene,  and  it  is  very  unlikely  that 
Bailly  would  have  troubled  him  with  these  letters. 


H  a 


100  A  BUDGET   OF   PAEADOXES. 

An  inquiry  into  the  cause  of  motion,  or  a  general  theory  of 
physics.     By  S.  Miller.     London,  1781,  4to. 

Newton  all  wrong :  matter  consists  of  two  kinds  of  particles, 
one  inert,  the  other  elastic  and  capable  of  expanding  themselves 
ad  infinitum. 

Des  Erreurs  et  de  la  Verite,  ou  les  hommes  rappeles  au  prin- 
cipe  universel  de  la  science ;  ouvrage  dans  lequel,  en  faisant 
remarquer  aux  observateurs  1'incertitude  de  leurs  recherches, 
et  leurs  meprises  continuelles,  on  leur  indique  la  route  qu'ils 
auroient  du.  suivre,  pour  acquerir  1'evidence  physique  sur 
1'origine  du  bien  et  du  mal,  sur  l'homme,  sur  la  nature  matcrielle, 
et  la  nature  sacree ;  sur  la  base  des  gouvernements  politiques, 
sur  1'autorite  des  souverains,  sur  la  justice  civile  et  criininellc, 
sur  les  sciences,  les  langues,  et  les  arts.  Par  un  Ph.  .  .  . 
Inc.  ...  A  Edimbourg.  1782.  Two  vols.  8vo. 

This  is  the  famous  work  of  Louis  Claude  de  Saint-Martin 
(1743-1803),  for  whose  other  works,  vagaries  included,  the  reader 
must  look  elsewhere  :  among  other  things,  he  was  a  translator  of 
Jacob  Behrnen.  The  title  promises  much,  and  the  writer  has 
smart  thoughts  now  and  then ;  but  the  whole  is  the  wearisome 
omniscience  of  the  author's  day  and  country,  which  no  reader  of 
our  time  can  tolerate.  Not  that  we  dislike  omniscience ;  but 
we  have  it  of  our  own  country,  both  home-made  and  imported  ; 
and  fashions  vary.  But  surely  there  can  be  but  one  omniscience  ? 
Must  a  man  have  but  one  wife  ?  Nay,  may  not  a  man  have  a 
new  wife  while  the  old  one  is  living  ?  There  was  a  famous 
instrumental  professor  forty  years  ago,  who  presented  a  friend  to 

Madame .     The   friend  started,   and  looked  surprised ;  for, 

not  many  weeks  before,  he  had  been  presented  to  another  lady, 
with  the  same  title,  at  Paris.  The  musician  observed  his 

surprise,  and  quietly  said,   '  Celle-ci  est  Madame de  Lon- 

dres.'  In  like  manner  we  have  a  London  omniscience  now 
current,  which  would  make  any  one  start  who  only  knew  the  old 
French  article. 

The  book  was  printed  at  Lyon,  but  it  was  a  trick  of  French 
authors  to  pretend  to  be  afraid  of  prosecution :  it  made  a  book 
look  wicked-like  to  have  a  feigned  place  of  printing,  and  stimu- 
lated readers.  A  Government  which  had  undergone  Voltaire 
would  never  have  drawn  its  sword  upon  quiet  Saint-Martin.  To 
make  himself  look  still  worse,  he  was  only  ph[ilosophe]  Inc.  .  .  , 
which  is  generally  read  Inconnu,  but  sometimes  Incredule : 


SAINT-MARTIN.  101 

most  likely  the  ambiguity  was  intended.  There  is  an  awful 
paradox  about  the  book,  which  explains,  in  part,  its  leaden  same- 
ness. It  is  all  about  Vhomme,  Vhomme,  Vhomme,  except  as  much 
as  treats  of  les  homines,  les  hommes,  les  hommes ;  but  not  one 
single  man  is  mentioned  by  name  in  its  500  pages.  It  reminds 
one  of 

Water,  water,  everywhere, 

And  not  a  drop  to  drink. 

Not  one  opinion  of  any  other  man  is  referred  to,  in  the  way  of 
agn-emcnt  or  of  opposition.  Not  even  a  town  is  mentioned  : 
there  is  nothing  which  brings  a  capital  letter  into  the  middle  of  a 
sentence,  except,  by  the  rarest  accident,  siich  a  personification  as 
Justice.  A  likely  book  to  want  an  Edimbourg  godfather ! 

Saint-Martin  is  great  in  mathematics.  The  number  four 
essentially  belongs  to  straight  lines,  and  nine  to  curves.  The 
object  of  a  straight  line  is  to  perpetuate  ad  infinitum  the  pro- 
duction of  a  point  from  which  it  emanates.  A  circle  O  bounds 
the  production  of  all  its  radii,  tends  to  destroy  them,  and  is  in 
some  sort  their  enemy.  How  is  it  possible  that  things  so  distinct 
should  not  be  distinguished  in  their  number  as  well  as  in  their 
action  ?  If  this  important  observation  had  been  made  earlier, 
immense  trouble  would  have  been  saved  to  the  mathematicians, 
who  would  have  been  prevented  from  searching  for  a  common 
measure  to  lines  which  have  nothing  in  common.  But,  though 
all  straight  lines  have  the  number  four,  it  must  not  be  supposed 
that  they  are  all  equal,  for  a  line  is  the  result  of  its  law  and  its 
number  ;  but  though  both  are  the  same  for  all  lines  of  a  sort, 
they  act  differently,  as  to  force,  energy,  and  duration,  in  different 
individuals ;  which  explains  all  differences  of  length,  &c.  I 
congratulate  the  reader  who  understands  this  ;  and  I  do  not  pity 
the  one  who  does  not. 

Saint-Martin  and  his  works  are  now  as  completely  forgotten  as 
if  they  had  never  been  born,  except  so  far  as  this,  that  some  one 
may  take  up  one  of  the  works  as  of  heretical  character,  and  lay  it 
down  in  disappointment,  with  the  reflection  that  it  is  as  dull  as 
orthodoxy.  For  a  person  who  was  once  in  some  vogue,  it  would 
be  difficult  to  pick  out  a  more  fossil  writer,  from  Aa  to  Zypoeus, 
except, — though  it  is  unusual  for  (, — )  to  represent  an  interval  of 
more  than  a  year — his  unknown  opponent.  This  opponent,  in  the 
very  year  of  the  '  Des  Erreurs  .  .  .  .'  published  a  book  in  two 
parts  with  the  same  fictitious  place  of  printing ; 


102  A   BUDGET   OF   PARADOXES. 


Tableau  Naturel  des  Rapports  qui  existent  entre  Dieu,  1'Horame, 
et  1'Univers.     A  Edimbourg,  1782,  8vo. 

There  is  a  motto  from  the  Des  Erreurs  itself,  '  Expliquer  les 
choses  par  I'homme,  et  non  1'homme  par  les  choses.  Des  Erreurs 
et  de  la  Verite,  par  un  PH.  .  .  .  INC.  .  .  .,  p.  9.'  This  work  is  set 
down  in  various  catalogues  and  biographies  as  written  by  the 
PH.  .  .  .  INC.  .  .  .  himself.  But  it  is  not  usual  for  a  writer  to 
publish  two  works  in  the  same  year,  one  of  which  takes  a  motto 
from  the  other.  And  the  second  work  is  profuse  in  capitals  and 
italics,  and  uses  Hebrew  learning :  its  style  differs  much  from  the 
first  work.  The  first  work  sets  out  from  man,  and  has  nothing 
to  do  with  Grod :  the  second  is  religious  and  raps  the  knuckles  of 
the  first  as  follows : — '  Si  nous  voulons  nous  preserver  de  toutes 
les  illusions,  et  surtout  des  amorces  de  1'orgueil  par  lesquelles 
1'homme  est  si  souvent  seduit,  ne  prenons  jamais  les  homines, 
mais  toujours  Dieu  pour  notre  terme  de  comparaison.'  The  first 
uses  four  and  nine  in  various  ways,  of  which  I  have  quoted  one  : 
the  second  says,  '  Et  ici  se  trouve  deja  ime  explication  des 
nombres  quatre  et  neuf,  qui  ont  peu  embarrasse  dans  1'ouvrage  deja 
cite.  L'homme  s'est  egare  en  allant  de  quatre  a  neuf  .  .  .  .' 
The  work  cited  is  the  Erreurs,  &c.,  and  the  citation  is  in  the 
motto,  which  is  the  text  of  the  opposition  sermon. 

Method  to  discover  the  difference  of  the  earth's  diameters ; 
proving  its  true  ratio  to  be  not  less  variable  than  as  45  is  to  46, 
and  shortest  in  its  pole's  axis  174  miles  .  .  .  likewise  a  method 
for  fixing  an  universal  standard  for  weights  and  measures.  By 
Thomas  Williams.  London,  1788,  8vo. 

Mr.  Williams  was  a  paradoxer  in  his  day,  and  proposed  what 
was,  no  doubt,  laughed  at  by  some.  He  proposed  the  sort  of  plan 
which  the  French — independently  of  course — carried  into  effect  a 
few  years  after.  He  would  have  the  52nd  degree  of  latitude 
divided  into  100,000  parts  and  each  part  a  geographical  yard. 
The  geographical  tun  was  to  be  the  cube  of  the  geographical 
yard  filled  with  sea-water  taken  some  leagues  from  land.  All 
multiples  and  subdivisions  were  to  be  decimal. 

I  was  beginning  to  look  up  those  who  had  made  similar 
proposals,  when  a  learned  article  .on  the  proposal  of  a  metrical 
system  came  under  my  eye  in  the  Times  of  Sept.  15,  1863.  The 
author  cites  Mouton,  who  would  have  the  minute  of  a  degree 
divided  into  10,000  virgulce;  James  Cassini,  whose  foot  was  to  be 


PAINE— WOLLSTONECE  AFT— PAKR.  103 

six  thousandths  of  a  minute ;  and  Paucton,  whose  foot  was  the 
400,000th  of  a  degree.  I  have  verified  the  first  and  third  state- 
ments ;  surely  the  second  ought  to  be  the  six-thousandth. 

An  inquiry  into  the  Copernican  system  .  .  .  wherein  it  is 
proved,  in  the  clearest  manner,  that  the  earth  has  only  her 
diurnal  motion  .  .  .  with  an  attempt  to  point  out  the  only  true 
way  whereby  mankind  can  receive  any  real  benefit  from  the 
study  of  the  heavenly  bodies.  By  John  Cunningham.  London, 
]  789,  8vo. 

The  '  true  way '  appears  to  be  the  treatment  of  heaven  and 
earth  as  emblematical  of  the  Trinity. 

Cosmology.  An  inquiry  into  the  cause  of  what  is  called  gra- 
vitation or  attraction,  in  which  the  motions  of  the  heavenly 
bodies,  and  the  preservation  and  operations  of  all  nature,  are 
deduced  from  an  universal  principle  of  efflux  and  reflux.  By 
T.  Vivian,  vicar  of  Corn  wood,  Devon.  Bath,  1792,  12mo. 

Attraction,  an  influx  of  matter  to  the  sun  ;  centrifugal  force, 
the  solar  rays ;  cohesion,  the  pressure  of  the  atmosphere.  The 
confusion  about  centrifugal  force,  so  called,  as  demanding  an 
external  agent,  is  very  common. 

The  rights  of  MAN,  being  an  answer    to  Mr.   Burke's  attack  on 

the    French   Revolution.     By  Thomas   Paine.     In   two   parts. 

1791-1792.     8vo.     (Various  editions.) 
A    vindication  of    the    rights     of    WOMAN,   with    strictures    on 

political  and  moral  subjects.     By  Mary  Wollstonecraft.     1792. 

8vo. 
A   sketch   of  the   rights   of  BOYS    and   GIRLS.      By    Launcelot 

Light,    of  Westminster    School ;    and    Laetitia    Lookabout,    of 

Queen's   Square,    Bloomsbury.       [By   the   Rev.   Samuel  Parr, 

LL.D.]     1792.    8vo.  (pp.  64). 

When  did  we  three  meet  before  ?  The  first  work  has  sunk  into 
oblivion :  had  it  merited  its  title,  it  might  have  lived.  It  is  what 
the  French  call  a  piece  de  circonstance ;  it  belongs  in  time  to  the 
French  Revolution,  and  in  matter  to  Burke's  opinion  of  that 
movement.  Those  who  only  know  its  name  think  it  was  really 
an  attempt  to  write  a  philosophical  treatise  on  what  we  now  call 
socialism.  Silly  government  prosecutions  gave  it  what  it  never 
could  have  got  for  itself. 

Mary  Wollstonecraft  seldom  has  her  name  spelt  right.  I 
suppose  the  0  !  O !  character  she  got  made  her  Woolstonecraft. 


104  A  BUDGET   OF   PARADOXES. 

Watt  gives  double  insinuation,  for  his  cross-reference  sends  us  to 
Goodwin.  No  doubt  the  title  of  the  book  was  an  act  of  disciple- 
ship  to  Paine's  '  Rights  of  Man ' ;  but  this  title  is  very  badly 
chosen.  The  book  was  marred  by  it,  especially  when  the  authoress 
and  her  husband  assumed  the  right  of  dispensing  with  legal 
sanction  until  the  appfoach  of  offspring  brought  them  to  a  sense 
of  their  child's  interest.  Not  a  hint  of  such  a  claim  is  found  in 
the  book,  which  is  mostly  about  female  education.  The  right 
claimed  for  woman  is  to  have  the  education  of  a  rational  human 
being,  and  not  to  be  considered  as  nothing  but  woman  throughout 
youthful  training.  The  maxims  of  Mary  Wollstonecraft  are  now, 
though  not  derived  from  her,  largely  followed  in  the  education  of 
girls,  especially  in  home  education :  just  as  many  of  the  political 
principles  of  Tom  Paine,  again  not  derived  from  him,  are  the 
guides  of  our  actual  legislation.  I  remember,  forty  years  ago, 
an  old  lady  who  used  to  declare  that  she  disliked  girls  from  the 
age  of  sixteen  to  five-and-twenty.  '  They  are  full,'  said  she,  '  of 
femalities.'  She  spoke  of  their  behaviour  to  women  as  well  as  to 
men.  She  would  have  been  shocked  to  know  that  she  was  a 
follower  of  Mary  Wollstonecraft,  and  had  packed  half  her  book 
into  one  sentence. 

The  third  work  is  a  satirical  attack  on  Mary  Wollstonecraft  and 
Tom  Paine.  The  details  of  the  attack  would  convince  any  one 
that  neither  has  anything  which  would  now  excite  reprobation. 
It  is  utterly  unworthy  of  Dr.  Parr,  and  has  quite  disappeared 
from  lists  of  his  works,  if  it  were  ever  there.  That  it  was  written 
by  him  I  take  to  be  evident,  as  follows.  Nichols,  who  could  not 
fail  to  know,  says  (Anecd.,  vol.  ix.  p.  120):  'This  is  a  playful 
essay  by  a  first-rate  scholar,  who  is  elsewhere  noticed  in  this 
volume,  but  whose  name  I  shall  not  bring  forward  on  so  trifling 
an  occasion.'  Who  the  scholar  was  is  made  obvious  by  Master 
Launcelot  being  made  to  talk  of  Bellendenus.  Further,  the 
same  boy  is  made  to  say,  '  Let  Dr.  Parr  lay  his  hand  upon  his 
heart,  if  his  conscience  will  let  him,  and  ask  himself  how  many 
thousands  of  waggon-loads  of  this  article  [birch]  he  has  cruelly 
misapplied.'  How  could  this  apply  to  Parr,  with  his  handful  of 
private  pupils,  and  no  reputation  for  severity  ?  Any  one  except 
himself  would  have  called  on  the  head-master  of  Westminster  or 
Eton.  I  doubt  whether  the  name  of  Parr  could  be  connected 
with  the  rod  by  anything  in  print,  except  the  above  and  an 
anecdote  of  his  pupil,  Tom  Sheridan.  The  Doctor  had  dressed 
for  a  dinner  visit,  and  was  ready  a  quarter  of  an  hour  too  soon  to 
set  off.  « Tom,'  said  he,  « I  think  I  had  better  whip  you  now ; 


SAMUEL   PARR.  105 

you  are  sure  to  do  something  while  I  am  out.' — '  I  wish  you  would, 
sir ! '  said  the  boy  ;  '  it  would  be  a  letter  of  licence  for  the  whole 
evening-.'  The  Doctor  saw  the  force  of  the  retort :  my  two 
tutelaries  will  see  it  by  this  time.  They  paid  in  advance  ;  and  I 
have  given  liberal  interpretation  to  the  order. 

The  following  story  of  Dr.  Parr  was  told  me  and  others,  about 
1829,  by  the  late  Leonard  Homer,  who  knew  him  intimately. 
Parr  was  staying  in  a  house  full  of  company,  I  think  in  the 
north  of  England.  Some  gentlemen  from  America  were  among 
the  guests,  and  after  dinner  they  disputed  some  of  Parr's  asser- 
tions or  arguments.  So  the  Doctor  broke  out  with  '  Do  you 
know  what  country  you  come  from  ?  You  come  from  the  place 
to  which  we  used  to  send  our  thieves ! '  This  made  the  host 
angry,  and  he  gave  Parr  such  a  severe  rebuke  as  sent  him  irom 
the  room  in  ill-humour.  The  rest  walked  on  the  lawn,  amusing 
the  Americans  with  sketches  of  the  Doctor.  There  was  a  dark 
cloud  overhead,  and  from  that  cloud  presently  came  a  voice 
which  called  Tham  (Parr-lisp  for  Sam).  The  company  were 
astonished  for  a  moment,  but  thought  the  Doctor  was  calling  his 
servant  in  the  house,  and  that  the  apparent  direction  was  an 
illusion  arising  out  of  inattention.  But  presently  the  sound  was 
repeated,  certainly  from  the  cloud, 

And  nearer,  clearer,  deadlier  than  before. 

There  was  now  a  little  alarm  :  where  could  the  Doctor  have  got 
to  ?  They  ran  to  his  bedroom,  and  there  they  discovered  a 
sufficient  rather  than  satisfactory  explanation.  The  Doctor  had 
taken  his  pipe  into  his  bedroom,  and  had  seated  himself,  in  sulky 
mood,  upon  the  higher  bar  of  a  large  and  deep  old-fashioned 
grate  with  a  high  mantelshelf.  Here  he  had  tumbled  backwards, 
and  doubled  himself  up  between  the  bars  and  the  back  of  the 
grate.  He  was  fixed  tight,  and  when  he  called  for  help,  he  could 
only  throw  his  voice  up  the  chimney.  The  echo  from  the  cloud 
was  the  warning  which  brought  his  friends  to  the  rescue. 

Days  of  political  paradox  were  coming,  at  which  we  now  stare. 
Cobbett  said,  about  1830,  in  earnest,  that  in  the  country  every 
man  who  did  not  take  off  his  hat  to  the  clergyman  was  suspected, 
and  ran  a  fair  chance  of  having  something  brought  against  him. 
I  heard  this  assertion  canvassed,  when  it  was  made,  in  a  party  of 
elderly  persons.  The  Radicals  backed  it,  the  old  Tories  rather 
denied  it,  but  in  a  way  which  satisfied  me  they  ought  to  have 
denied  it  less  if  they  could  not  deny  it  more.  But  it  must  be 
said  that  the  Governments  stopped  far  short  of  what  their 


106  A  BUDGET   OF   PARADOXES. 

partisans  would  have  had  them  do.  All  who  know  Robert 
Robinson's  very  quiet  assault  on  church-made  festivals  in  hi 
'  History  and  Mystery  of  Good  Friday '  (1777)  will  hear  or 
remember  with  surprise  that  the  British  Critic  pronounced  it 
a  direct,  unprovoked,  and  malicious  libel  on  the  most  sacred 
institutions  of  the  national  Church.  It  was  reprinted  again  and 
again:  in  1811  it  was  in  a  cheap  form  at  6s  6^.  a  hundred. 
When  the  Jacobin  day  came,  the  State  was  really  in  a  fright : 
people  thought  twice  before  they  published  what  would  now  be 
quite  disregarded.  I  examined  a  quantity  of  letters  addressed  to 
George  Dyer  (Charles  Lamb's  G.D.)  and  what  between  the  auto- 
graphs of  Thelwall,  Hardy,  Home  Tooke,  and  all  the  rebels, 
put  together  a  packet  which  produced  five  guineas,  or  there- 
abouts, for  the  widow.  Among  them  were  the  following  verses, 
sent  by  the  author — who  would  not  put  his  name,  even  in  a 
private  letter,  for  fear  of  accidents — for  consultation  whether  they 
could  safely  be  sent  to  an  editor  :  and  they  were  not  sent.  The 
occasion  was  the  public  thanksgiving  at  St.  Paul's  for  the  naval 
victories,  December  19,  1797. 

God  bless  me  !  what  a  thing  ! 
Have  you  heard  that  the  King 

Goes  to  St.  Paul's  ? 
Good  Lord  !  and  when  he's  there, 
He'll  roll  his  eyes  in  prayer, 
To  make  poor  Johnny  stare 

At  this  fine  thing. 

No  doubt  the  plan  is  wise 
To  blind  poor  Johnny's  eyes 

By  this  grand  show ; 
For  should  he  once  suppose 
That  he's  led  by  the  nose, 
Down  the  whole  fabric  goes, 

Church,  lords,  and  king. 

As  he  shouts  Duncan's  praise, 
Mind  how  supplies  they'll  raise 

In  wondrous  haste. 
For  while  upon  the  sea 
We  gain  one  victory, 
John  still  a  dupe  will  be 

And  taxes  pay. 

Till  from  his  little  store 
Three-fourths  or  even  more 
Goes  to  the  Crown. 


WILLIAM   HONE'S   TRIALS,  107 

Ah,  John  !  you  little  think 
How  fast  we  downward  sink 
And  touch  the  fatal  brink 
At  which  we're  slaves. 

I  would  have  indicted  the  author  for  not  making  his  thirds 
and  sevenths  rhyme.  As  to  the  rhythm,  it  is  not  much  better 
than  what  the  French  sang  in  the  Calais  theatre,  when  the  Duke 
of  Clarence  took  over  Louis  XVIII.  in  1814. 

God  save  noble  Clarence, 

Who  brings  our  king  to  France  ; 

God  save  Clarence  ! 
He  maintains  the  glory 
Of  the  British  navy. 
&c.  &c. 

Perhaps  had  this  been  published,  the  Government  would  have 
assailed  it  as  a  libel  on  the  church  service.  They  got  into  the 
way  of  defending  themselves  by  making  libels  on  the  Church,  of 
what  were  libels,  if  on  anything,  on  the  rulers  of  the  State  ;  until 
the  celebrated  trials  of  Hone  settled  the  point  for  ever,  and 
established  that  juries  will  not  convict  for  one  offence,  even 
though  it  have  been  committed,  when  they  know  the  prosecution 
is  directed  at  another  offence  and  another  intent. 

The  results  of  Hone's  trials  (William  Hone,  1779-1842)  are 
among  the  important  constitutional  victories  of  our  century.  He 
published  parodies  on  the  Creeds,  the  Lord's  Prayer,  the  Cate- 
chism, &c.,  with  intent  to  bring  the  Ministry  into  contempt : 
everybody  knew  that  was  his  purpose.  The  Government  indicted 
him  for  impious,  profane,  blasphemous  intent,  but  not  for 
seditious  intent.  They  hoped  to  wear  him  out  by  proceeding  day 
by  day.  December  18,  1817,  they  hid  themselves  under  the 
Lord's  Prayer,  the  Creed,  and  the  Commandments ;  December  1 9, 
under  the  Litany  ;  December  20,  under  the  Athanasian  Creed, 
an  odd  place  for  shelter  when  they  could  not  find  it  in  the  previous 
places.  Hone  defended  himself  for  six,  seven,  and  eight  hours  on 
the  several  days:  and  the  jury  acquitted  him  in  15,  105,  and  20 
minutes.  In  the  second  trial  the  offence  was  laid  both  as  pro- 
fanity and  as  sedition,  which  seems  to  have  made  the  jury  hesitate. 
And  they  probably  came  to  think  that  the  second  count  was  false 
pretence :  but  the  length  of  their  deliberation  is  a  satisfactory 
addition  to  the  value  of  the  whole.  In  the  first  trial  the  Attorney- 
General  (Shepherd)  had  the  impudence  to  say  that  the  libel 
had  nothing  of  a  political  tendency  about  it,  but  was  avowedly 


108  A   BUDGET   OF  PAEADOXES 

set  off  against  the  religion  and  worship  of  the  Church  of  England. 
The  whole  is  political  in  every  sentence ;  neither  more  nor  less 
political  than  the  following,  which  is  part  of  the  parody  on  the 
Catechism.  '  What  is  thy  duty  towards  the  Minister  ?  My  duty 
towards  the  Minister  is,  to  trust  him  as  much  as  I  can  ;  to  honour 
him  with  all  my  words,  with  all  my  bows,  with  all  my  scrapes, 
and  with  all  my  cringes ;  to  flatter  him  ;  to  give  him  thanks ;  to 
give  up  my  whole  soul  to  him ;  to  idolize  his  name,  and  obey  his 
word,  and  serve  him  blindly  all  the  days  of  his  political  life.' 
And  the  parody  on  the  Creed  begins,  '  I  believe  in  George,  the 
Regent  almighty,  maker  of  new  streets  and  Knights  of  the  Bath.' 
This  is  what  the  Attorney- General  said  had  nothing  of  a  political 
tendency  about  it.  But  this  was  on  the  first  trial :  Hone 
was  not  known.  The  first  day's  trial  was  under  Justice  Abbott 
(afterwards  C.  J.  Tenterden).  It  was  perfectly  understood,  when 
Chief  Justice  Ellenborough  appeared  in  Court  on  the  second  day, 
that  he  was  very  angry  at  the  first  result,  and  put  his  junior  aside 
to  try  his  own  rougher  dealing.  But  Hone  tamed  the  lion.  An 
eye-witness  told  me  that  when  he  implored  of  Hone  not  to  detail 
his  own  father  Bishop  Law's  views  on  the  Athanasian  Creed,  which 
humble  petition  Hone  kindly  granted,  he  held  by  the  desk  for 
support.  And  the  same  when — which  is  not  reported — the 
Attorney-General  appealed  to  the  Court  for  protection  against  a 
stinging  attack  which  Hone  made  on  the  Bar :  he  held  on,  and 
said,  '  Mr.  Attorney,  what  can  I  do  ! '  I  was  a  boy  of  twelve  years 
old,  but  so  strong  was  the  feeling  of  exultation  at  the  verdicts 
that  boys  at  school  were  not  prohibited  from  seeing  the  parodies, 
which  would  have  been  held  at  any  other  time  quite  unfit  to 
meet  their  eyes.  I  was  not  able  to  comprehend  all  about  the 
Lord  Chief  Justice  until  I  read  and  heard  again  in  after  years. 
In  the  meantime,  Joe  Miller  had  given  me  the  story  of  the 
leopard  which  was  sent  home  on  board  a  ship  of  war,  and  was  in 
two  days  made  as  docile  as  a  cat  by  the  sailors.  '  You  have  got 
that  fellow  well  under,'  said  an  officer.  'Lord  bless  your  honour !' 
said  Jack,  '  if  the  Emperor  of  Marocky  would  send  us  a  cock 
rhinoceros,  we'd  bring  him  to  his  bearings  in  no  time  ! '  When  I 
came  to  the  subject  again,  it  pleased  me  to  entertain  the  question 
whether,  if  the  Emperor  had  sent  a  cock  rhinoceros  to  preside  on 
the  third  day  in  the  King's  Bench,  Hone  would  have  mastered 
him :  I  forget  how  I  settled  it.  There  grew  up  a  story  that  Hone 
caused  Lord  Ellenborough's  death,  but  this  could  not  have  been 
true.  Lord  Ellenborough  resigned  his  seat  in  a  few  months,  and 


SUBSCRIPTIONS   FOR   HONE.  109 

died  just  a  year  after  the  trials  ;  but  sixty-eight  years  may  have 
had  more  to  do  with  it  than  his  defeat. 

A  large  subscription  was  raised  for  Hone,  headed  by  the  Duke 
of  Bedford  for  105Z.  Many  of  the  leading  ante-ministerialists 
joined  :  but  there  were  many  of  the  other  side  who  avowed  their 
disapprobation  of  the  false  pretence.  Many  could  not  venture 
their  names.  In  the  list  I  find :  A  member  of  the  House  of  Lords, 
an  enemy  to  persecution,  and  especially  to  religious  persecution 
employed  for  political  purposes — No  parodist,  but  an  enemy  to 
persecution — A  juryman  on  the  third  day's  trial—  Ellen  Borough 
— My  name  would  ruin  me — Oh  !  minions  of  Pitt — Oil  for  the 
Hone — The  Ghosts  of  Jeffries  and  Sir  William  Roy  [Ghosts  of 
Jeffries  in  abundance] — A  conscientious  Jury  and  a  conscientious 
Attorney,  ll.  6s.  Sd. — To  Mr.  Hone,  for  defending  in  his  own 
person  the  freedom  of  the  press,  attacked  for  a  political  object, 
under  the  old  pretence  of  supporting  Eeligion — A  cut  at  corruption 
— An  Earldom  for  myself  and  a  translation  for  my  brother — One 
who  disapproves  of  parodies,  but  abhors  persecution — From  a 
schoolboy  who  wishes  Mr.  Hone  to  have  a  very  grand  subscription 
— *  For  delicacy's  sake  forbear,'  and  '  Felix  trembled ' —  'I  will  go 
myself  to-morrow ' — Judge  Jeffries'  works  rebound  in  calf  by  Law 
— Keep  us  from  Law,  and  from  the  Shepherd's  paw — I  must  not 
give  you  my  name,  but  God  bless  you ! — As  much  like  Judge 
Jeffries  as  the  present  times  will  permit — May  Jeffries'  fame 
and  Jeffries'  fate  on  every  modern  Jeffries  wait — No  parodist, 
but  an  admirer  of  the  man  who  has  proved  the  fallacy  of  the 
Lawyer's  Law,  that  when  a  man  is  his  own  advocate  he  has  a  fool 
for  his  client — A  Mussulman  who  thinks  it  would  not  be  an  impious 
libel  to  parody  the  Koran — May  the  suspenders  of  the  Habeas 
Corpus  Act  be  speedily  suspended — Three  times  twelve  for  thrice- 
tried  Hone,  who  cleared  the  cases  himself  alone,  and  won  three 
heats  by  twelve  to  one,  \l.  16s. — A  conscientious  attorney, 
11.  6s.  Sd.— Rev.  T.  B.  Morris,  rector  of  Shelfanger,  who  dis- 
approves of  the  parodies,  but  abhors  the  making  an  affected  zeal 
for  religion  the  pretext  for  political  persecution — A  Lawyer 
opposed  in  principle  to  Law — For  the  Hone  that  set  the  razor 
that  shaved  the  rats — Rev.  Dr.  Samuel  Parr,  who  most  seriously 
disapproves  of  all  parodies  upon  the  hallowed  language  of  Scripture 
and  the  contents  of  the  Prayer-book,  but  acquits  Mr.  Hone  of 
intentional  impiety,  admires  his  talents  and  fortitude,  and 
applauds  the  good  sense  and  integrity  of  his  juries— Religion 
without  hypocrisy,  and  Law  without  partiality — 0  Law  !  0  Law  ? 
0  Law ! 


110  A   BUDGET  OF  PARADOXES. 

These  are  specimens  of  a  great  many  allusive  mottoes.  The 
subscription  was  very  large,  and  would  have  bought  a  handsome 
annuity,  but  Hone  employed  it  in  the  bookselling  trade,  and  did 
not  thrive.  His  '  Everyday  Book '  and  his  '  Apocryphal  New 
Testament '  are  useful  books.  On  an  annuity  he  would  have 
thriven  as  an  antiquarian  writer  and  collector.  It  is  well  that 
the  attack  upon  the  right  to  ridicule  Ministers  roused  a  dormant 
power  which  was  equal  to  the  occasion.  Hone  declared,  on  his 
honour,  that  he  had  never  addressed  a  meeting  in  his  life,  nor 
spoken  a  word  before  more  than  twelve  persons.  Had  he — which 
however  could  not  then  be  done — employed  counsel,  and  had  a 
guilty  defence  made  for  him,  he  would  very  likely  have  been 
convicted,  and  the  work  would  have  been  left  to  be  done  by 
another.  No  question  that  the  parodies  disgusted  all  who 
reverenced  Christianity,  and  who  could  not  separate  the  serious  and 
the  ludicrous,  and  prevent  their  existence  in  combination. 

My  extracts,  &c.,  are  from  the  nineteenth,  seventeenth,  and  six- 
teenth editions  of  the  three  trials,  which  seem  to  have  been  con- 
temporaneous (all  in  1818)  as  they  are  made  up  into  one  book, 
with  additional  title  over  all,  and  the  motto  '  Thrice  the  brindled 
cat  hath  mew'd.'  They  are  published  by  Hone  himself,  who  I 
should  -have  said  was  a  publisher  as  well  as  was  to  be.  And 
though  the  trials  only  ended  Dec.  20,  1817,  the  preface  attached 
to  this  common  title  is  dated  Jan.  23,  1818. 

The  spirit  which  was  roused  against  the  false  dealing  of 
the  Government,  i.e.  the  pretence  of  prosecuting  for  impiety 
when  all  the  world  knew  the  real  offence  was,  if  anything,  sedi- 
tion— was  not  got  up  at  the  moment :  there  had  been  previous 
exhibitions  of  it.  For  example,  in  the  spring  of  1 8 1 8  Mr.  Russell, 
a  little  printer  in  Birmingham,  was  indicted  for  publishing  the 
Political  Litany  on  which  Hone  was  afterwards  tried.  He  took 
his  witnesses  to  the  summer  Warwick  assizes,  and  was  told  that 
the  indictment  had  been  removed  by  certiorari  into  the  King's 
Bench.  He  had  notice  of  trial  for  the  spring  assizes  at  Warwick: 
he  took  his  witnesses  there,  and  the  trial  was  postponed  by  the 
Crown.  He  then  had  notice  for  the  summer  assizes  at  Warwick  ; 
and  so  on.  The  policy  seems  to  have  been  to  wear  out  the  ob- 
noxious parties,  either  by  delays  or  by  heaping  on  trials.  The 
Government  was  odious,  and  knew  it  could  not  get  verdicts  against 
ridicule,  and  could  get  verdicts  against  impiety.  No  difficulty 
was  found  in  convicting  the  sellers  of  Paine's  works,  and  the  like. 
When  Hone  was  held  to  bail  it  was  seen  that  a  crisis  was  at  hand. 
All  parties  in  politics  furnished  him  with  parodies  in  proof  of 


PROFANITY  OF  LORD  BYROX.  Ill 

religious  persons  having  made  instruments  of  them.  The  parodies 
by  Addison  and  Luther  were  contributed  by  a  Tory  lawyer,  who 
was  afterwards  a  judge. 

Hone  had  published,  in  1817,  tracts  of  purely  political  ridicule: 
'  official  account  of  the  noble  lord's  bite,'  *  trial  of  the  dog  for 
biting  the  noble  lord,'  &c.  These  were  not  touched.  After  the 

o  7 

trials,  it  is  manifest  that  Hone  was  to  be  unassailed,  do  what  he 
might.  '  The  Political  House  that  Jack  built,'  in  1 8 1 9  ;  «  The  Man 
in  the  Moon,'  1 820  ;  '  The  Queen's  Matrimonial  Ladder,'  '  Non  mi 
ricordo,'  'The  E— 1  fowls,'  1 820  ;  '  The  Political  Showman  at  home,' 
with  plates  by  G.  Cruickshank,  1821  [he  did  all  the  plates]  ;  '  The 
Spirit  of  Despotism,'  1821 — would  have  been  legitimate  marks 
for  prosecution  in  previous  years.  The  biting  caricature  of 
several  of  these  works  are  remembered  to  this  day.  '  The  Spirit 
of  Despotism'  was  a  tract  of  1795,  of  which  a  few  copies  had  been 
privately  circulated  with  great  secrecy.  Hone  reprinted  it,  and 
prefixed  the  following  address  to  '  Robert  Stewart,  alias  Lord 
Castlereagh ' — '  It  appears  to  me  that  if,  unhappily,  your  counsels 
are  allowed  much  longer  to  prevail  in  the  Brunswick  Cabinet, 
they  will  bring  on  a  crisis,  in  which  the  king  may  be  dethroned 
or  the  people  enslaved.  Experience  has  shown  that  the  people 
will  not  l>e  enslaved — the  alternative  is  the  affair  of  your  em- 
ployers.' Hone  might  say  this  without  notice. 

In  1819  Mr.  Murray  published  Lord  Byron's  'Don  Juan,'  and 
Hone  followed  it  with  '  Don  John,  or  Don  Juan  unmasked,'  a 
little  account  of  what  the  publisher  to  the  Admiralty  was  allowed 
to  issue  without  prosecution.  The  parody  on  the  Commandments 
was  a  case  very  much  in  point :  and  Hone  makes  a  stinging 
allusion  to  the  use  of  the  '  unutterable  Nvme,  with  a  profane 
levity  unsurpassed  by  any  other  two  lines  in  the  English  language.* 
The  lines  are 

'Tis  strange — the  Hebrew  noun  which  means  'I  am,' 
The  English  always  use  to  govern  d n. 

Hone  ends  with  : '  Lord  Byron's  dedication  of  "  Don  Juan  "  to  Lord 
Castlereagh  was  suppressed  by  Mr.  Murray  from  delicacy  to 
Ministers.  Q.  Why  did  not  Mr.  Murray  suppress  Lord  Byron's 
parody  on  the  Ten  Commandments?  A.  Because  it  contains 
nothing  in  ridicule  of  Ministers,  and  therefore  nothing  that  they 
could  suppose  would  lead  to  the  displeasure  of  Almighty  God.' 

The  little  matters  on  which  I  have  dwelt  will  never  appear  in 
history  from  their  political  importance,  except  in  a  few  words  of 
result.  As  a  mode  of  thought,  silly  evasions  of  all  kinds  belong 


112  A  BUDGET   OF   PARADOXES. 

to  such  a  work  as  the  present.  Ignorance,  which  seats  itself  in 
the  chair  of  knowledge,  is  a  mother  of  revolutions  in  politics,  and 
of  unread  pamphlets  in  circle-squaring.  From  1815  to  1830  the 
question  of  revolution  or  no  revolution  lurked  in  all  our  English 
discussions.  The  high  classes  must  govern ;  the  high  classes 
shall  not  govern  ;  and  thereupon  issue  was  to  be  joined.  In  1828- 
1833  the  question  came  to  issue;  and  it  was,  Eevolution  with  or 
without  civil  war ;  choose.  The  choice  was  wisely  made  ;  and 
the  Eeform  Bill  started  a  new  system  so  well  dovetailed  into  the 
old  that  the  joinings  are  hardly  visible.  And  now,  in  1867,  the 
thing  is  repeated  with  a  marked  subsidence  of  symptoms  ;  and  the 
party  which  has  taken  the  place  of  the  extinct  Tories  is  carrying 
through  Parliament  a  wider  extension  of  the  franchise  than  their 
opponents  would  have  ventured.  Napoleon  used  to  say  that  a 
decided  nose  was  a  sign  of  power :  on  which  it  has  been  remarked 
that  he  had  good  reason  to  say  so  before  the  play  was  done.  And 
so  had  our  country ;  it  was  saved  from  a  religious  war,  and  from 
a  civil  war,  by  the  power  of  that  nose  over  its  colleagues. 

The    Commentaries  of  Proclus.      Translated  by  Thomas  Taylor. 
London,  1792,  2  vols.  4to. 

The  reputation  of  '  the  Platonist '  begins  to  grow,  and  will 
continue  to  grow.  The  most  authentic  account  is  in  the  Penny 
Cyclopaedia,  written  by  one  of  the  few  persons  who  knew  him 
well,  and  one  of  the  fewer  who  possess  all  his  works.  At  page 
Ivi.  of  the  Introduction  is  Taylor's  notion  of  the  way  to  find  the 
circumference.  It  is  not  geometrical,  for  it  proceeds  on  the 
motion  of  a  point:  'the  words  '  on  account  of  the  simplicity  of  the 
impulsive  motion,  such  a  line  must  be  either  straight  or  circular' 
will  suffice  to  show  how  Platonic  it  is.  Taylor  certainly  professed 
a  kind  of  heathenism.  D'Israeli  said,  'Mr.  T.  Taylor,  the  Platonic 
philosopher  and  the  modern  Plethon,  consonant  to  that  philosophy, 
professes  polytheism.'  Taylor  printed  this  in  large  type,  in  a 
page  by  itself  after  the  dedication,  without  any  disavowal.  I 
have  seen  the  following,  Greek  and  translation  both,  in  his  hand- 
writing : — '  Has  dyaQos  rj  dyaSos  sQviKOs'  Kai  iras  ^pia-navos  y 
"XpicfTtavos  KaKus.  Every  good  man,  so  far  as  he  is  a  good  man, 
is  a  heathen  ;  and  every  Christian,  so  far  as  he  is  a  Christian,  is  a 
bad  man.'  Whether  Taylor  had  in  his  head  the  Christian  of  the 
New  Testament,  or  whether  he  drew  from  those  members  of  the 
'  religious  world '  who  make  manifest  the  religious  flesh  and  the 
religious  devil,  cannot  be  decided  by  us,  and  perhaps  was  not 
known  to  himself.  If  a  heathen,  he  was  a  virtuous  one. 


HANNAH  MORE -MISS  BURNEY.  113 

(1795.)  This  is  the  date  of  a  very  remarkable  paradox.  The 
religious  world — to  use  a  name  claimed  by  a  doctrinal  sect — 
had  long  set  its  face  against  amusing  literature,  and  all  works  of 
imagination.  Bunyan,  Milton,  and  a  few  others  were  irresis- 
tible ;  but  a  long  face  was  pulled  at  every  attempt  to  produce 
something  readable  for  poor  people  and  poor  children.  In 
1795,  a  benevolent  association  began  to  circulate  the  works  of 
a  lady  who  had  been  herself  a  dramatist,  and  had  nourished  a 
pleasant  vein  of  satire  in  the  society  of  Garrick  and  his  friends  ; 
all  which  is  carefully  suppressed  in  some  biographies.  Hannah 
More's  Cheap  Repository  Tracts,  which  were  bought  by  millions 
of  copies,  destroyed  the  vicious  publications  with  which  the 
hawkers  deluged  the  country,  by  the  simple  process  of  furnishing 
the  hawkers  with  something  more  saleable. 

Dramatic  fiction,  in  which  the  characters  are  drawn  by  them- 
selves, was,  at  the  middle  of  the  last  century,  the  monopoly  of 
writers  who  required  indecorum,  such  as  Fielding  and  Smollett. 
All,  or  nearly  all,  which  could  be  permitted  to  the  young,  was 
dry  narrative,  written  by  people  who  could  not  make  their 
personages  talk  character ;  they  all  spoke  alike.  The  author 
of  the  Rambler  is  ridiculed,  because  his  young  ladies  talk 
Johnsonese  ;  but  the  satirists  forget  that  all  the  presentable  novel- 
writers  were  equally  incompetent ;  even  the  author  of  '  Zeluco  ' 
(1789)  is  the  strongest  possible  case  in  point. 

Dr.  Moore,  the  father  of  the  hero  of  Corunna,  with  good  narra- 
tive power,  some  sly  humour,  and  much  observation  of  character, 
would  have  been,  in  our  day,  a  writer  of  the  Peacock  family. 
Nevertheless,  to  one  who  is  accustomed  to  our  style  of  things, 
it  is  comic  to  read  the  dialogue  of  a  jealous  husband,  a  suspected 
wife,  a  faithless  maid-servant,  a  tool  of  a  nurse,  a  wrong-headed 
pomposity  of  a  priest,  and  a  sensible  physician,  all  talking  Dr. 
Moore  through  their  masks.  Certainly  an  Irish  soldier  does  say 
by  Jasus,  and  a  cockney  footman  this  here  and  that  there ;  and 
this  and  the  like  is  all  the  painting  of  characters  which  is  effected 
out  of  the  mouths  of  the  bearers  by  a  narrator  of  great  power. 
I  suspect  that  some  novelists  repressed  their  power  under  a  rule 
that  a  narrative  should  narrate,  and  that  the  dramatic  should  be 
confined  to  the  drama. 

I  make  no  exception  in  favour  of  Miss  Burney ;  though  she  was 
the  forerunner  of  a  new  era.  Suppose  a  country  in  which  dress 
is  always  of  one  colour  ;  suppose  an  importer  who  brings  in  cargoes 
of  blue  stuff,  red  stuff,  green  stuff,  &c.,  and  exhibits  dresses  of 
these  several  colours,  that  person  is  the  similitude  of  Miss 

i 


114  A   BUDGET   OF  PAKADOXES. 

Burney.  It  would  be  a  delightful  change  from  a  universal  dull 
brown,  to  see  one  person  all  red,  another  all  blue,  &c. ;  but  the 
•  real  inventor  of  pleasant  dress  would  be  the  one  who  could  mix 
his  colours  and  keep  down  the  bright  and  gaudy.  Miss  Burney's 
introduction  was  so  charming,  by  contrast,  that  she  nailed  such  men 
as  Johnson,  Burke,  Grarrick,  &c.,  to  her  books.  But  when  a 
person  who  has  read  them  with  keen  pleasure  in  boyhood,  as  I 
did,  comes  back  to  them  after  a  long  period,  during  which  he 
has  made  acquaintance  with  the  great  novelists  of  our  century, 
three-quarters  of  the  pleasure  is  replaced  by  wonder  that  he  had 
not  seen  he  was  at  a  puppet-show,  not  at  a  drama.  Take  some 
labelled  characters  out  of  our  humourists,  let  them  be  put 
together  into  one  piece,  to  speak  only  as  labelled  :  let  there  be 
a  Dominie  with  nothing  but  'Prodigious  ! '  a  Dick  Swiveller  with 
nothing  but  adapted  quotations  ;  a  Dr.  Folliott  with  nothing 
but  sneers  at  Lord  Brougham  ;  and  the  whole  will  pack  up  into 
one  of  Miss  Burney's  novels. 

Maria  Edgeworth,  Sydney  Owenson  (Lady  Morgan),  Jane 
Austen,  Walter  Scott,  &c.,  are  all  of  our  century ;  as  are,  I 
believe,  all  the  Minerva  Press  novels,  as  they  were  called,  which 
show  some  of  the  power  in  question.  Perhaps  dramatic  talent 
found  its  best  encouragement  in  the  drama  itself.  But  I  cannot 
ascertain  that  any  such  power  was  directed  at  the  multitude, 
whether  educated  or  uneducated,  with  natural  mixture  of 
character,  under  the  restraints  of  decorum,  until  the  use  of  it 
by  two  religious  writers  of  the  school  called  '  evangelical,'  Han- 
nah More  and  Rowland  Hill.  The  Village  Dialogues,  though 
not  equal  to  the  Repository  Tracts,  are  in  many  parts  an  ap- 
proach, and  perhaps  a  copy ;  there  is  frequently  humorous  satire, 
in  that  most  effective  form,  self-display.  They  were  published  in 
1800,  and,  partly  at  least,  by  the  Religious  Tract  Society,  the 
lineal  successor  of  the  Repository  association,  though  knowing 
nothing  about  its  predecessor.  I  think  it  right  to  add  that 
Rowland  Hill  here  mentioned  is  not  the  regenerator  of  the 
Post  Office.  Some  do  not  distinguish  accurately  ;  I  have  heard 
of  more  than  one  who  took  me  to  have  had  a  logical  controversy 
with  a  diplomatist  who  died  some  years  before  I  was  born. 

A  few  years  ago,  an  attempt  was  made  by  myself  and  others 
to  collect  some  information  about  the  Cheap  Repository  (see 
Notes  and  Queries,  3rd  Series,  vi.  241,  290,  353 ;  Christian 
Observer,  Dec.  1864,  pp.  944-49).  It  appeared  that  after  the 
Religious  Tract  Society  had  existed  more  than  fifty  years,  a  friend 
presented  it  with  a  copy  of  the  original  prospectus  of  the  Rcposi- 


THE   EELIGIOUS   TEACT   SOCIETY.  115 

tory,  a  thing  the  existence  of  which  was  not  known.  In  this 
prospectus  it  is  announced  that  from  the  plan  '  will  be  carefully 
excluded  whatever  is  enthusiastic,  absurd,  or  superstitious.'  The 
*  evangelical '  party  had,  from  the  foundation  of  the  Eeligious 
Tract  Society,  regretted  that  the  Repository  Tracts  '  did  not 
contain  a  fuller  statement  of  the  great  evangelical  principles ;' 
while  in  the  prospectus  it  is  also  stated  that  '  no  cause  of  any 
particular  party  is  intended  to  be  served  by  it,  but  general 
Christianity  will  be  promoted  upon  practical  principles.'  This 
explains  what  has  often  been  noticed,  that  the  tracts  contain  a 
mild  form  of  the  '  evangelical '  doctrine,  free  from  that  more 
fervid  dogmitism  which  appears  in  the  Village  Dialogues;  and 
such  as  H.  More's  friend,  Bishop  Porteus — a  great  promoter  of 
the  scheme — might  approve.  The  Religious  Tract  Society  (in 
1863)  republished  some  of  H.  More's  tracts,  with  alterations, 
additions,  and  omissions  ad  libitum.  This  is  an  improper  way 
of  dealing  with  the  works  of  the  dead  ;  especially  when  the 
reprints  are  of  popular  works.  A  small  type  addition  to  the 
preface  contains :  '  Some  alterations  and  abridgments  have  been 
made  to  adapt  them  to  the  present  times  and  the  aim  of  the 
Religious  Tract  Society.'  I  think  every  publicity  ought  to  be 
given  to  the  existence  of  such  a  practice ;  and  I  reprint  what  I 
said  on  the  subject  in  Notes  and  Queries. 

Alterations  in  works  which  the  Society  republishes  are  a  neces- 
sary part  of  their  plan,  though  such  notes  as  they  should  judge 
to  be  corrective  would  be  the  best  way  of  proceeding.  But  the 
fact  of  alteration  should  be  very  distinctly  announced  on  the  title 
of  the  work  itself,  not  left  to  a  little  bit  of  small  type  at  the  end 
of  the  preface,  in  the  place  where  trade  advertisements,  or  direc- 
tions to  the  binder,  are  often  found.  And  the  places  in  which 
alteration  has  been  made  should  be  pointed  out,  either  by  marks 
of  omission,  when  omission  is  the  alteration,  or  by  putting  the 
altered  sentences  in  brackets,  when  change  has  been  made.  May 
any  one  alter  the  works  of  the  dead  at  his  own  discretion  ?  We 
all  know  that  readers  in  general  will  take  each  sentence  to  be 
that  of  the  author  whose  name  is  on  the  title;  so  that  a  correcting 
republisher  makes  use  of  his  author's  n-ame  to  teach  his  own 
variation.  The  tortuous  logic  of  '  the  trade,'  which  is  content 
when  '  the  world '  is  satisfied,  is  not  easily  answered,  any  more 
than  an  eel  is  easily  caught ;  but  the  Religious  Tract  Society  may 
be  convinced  [in  the  old  sense]  in  a  sentence.  On  which  course 
would  they  feel  most  safe  in  giving  their  account  to  the  God  of 
truth  ?  '  In  your  own  conscience,  now  ? ' 

i  -2 


116  A  BUDGET  OF  PAEADOXES. 

I  have  tracked  out  a  good  many  of  the  variations  made  by  the 
Religious  Tract  Society  in  the  recently  published  volume  of 
Repository  Tracts.  Most  of  them  are  doctrinal  insertions  or 
amplifications,  to  the  matter  of  which  Hannah  More  would  not 
have  objected — all  that  can  be  brought  against  them  is  the  want 
of  notice.  But  I  have  found  two  which  the  respect  I  have  for  the 
Religious  Tract  Society,  in  spite  of  much  difference  on  various 
points,  must  not  prevent  my  designating  as  paltry.  In  the  story 
of  Mary  Wood,  a  kind-hearted  clergyman  converses  with  the  poor 
girl  who  has  ruined  herself  by  lying.  In  the  original,  he  '  assisted 
her  in  the  great  work  of  repentance  ; '  in  the  reprint  it  is  to  be 
shown  in  some  detail  how  he  did  this.  He  is  to  begin  by  pointing 
out  that  '  the  heart  is  deceitful  above  all  things  and  desperately 
wicked.'  Now  the  clergyman's  name  is  Heartwell :  so  to  prevent 
his  name  from  contradicting  his  doctrine,  he  is  actually  cut  down 
to  Harwell.  Hannah  More  meant  this  good  man  for  one  of  those 
described  in  Acts  xv.  8,  9,  and  his  name  was  appropriate. 

Again,  Mr.  Flatterwell,  in  persuasion  of  Parley  the  porter  to 
let  him  into  the  castle,  declares  that  the  worst  he  will  do  is  to 
'  play  an  innocent  game  of  cards  just  to  keep  you  awake,  or  sing 
a  cheerful  song  with  the  maids.'  Oh  fie  !  Miss  Hannah  More  ! 
and  you  a  single  lady  too,  and  a  contemporary  of  the  virtuous 
Bowdler  !  Though  Flatterwell  be  an  allegory  of  the  devil,  this 
is  really  too  indecorous,  even  for  him.  Out  with  the  three  last 
words !  and  out  it  is. 

The  Society  cuts  a  poor  figure  before  a  literary  tribunal. 
Nothing  was  wanted  except  an  admission  that  the  remarks  made  by 
me  were  unanswerable,  and  this  was  immediately  furnished  by  the 
Secretary  (N.  and  Q.  3  S.  vi.  290).  In  a  reply  of  which  six  parts 
out  of  seven  are  a  very  amplified  statement  that  the  Society  did 
not  intend  to  reprint  all  Hannah  More's  tracts,  the  remaining 
seventh  is  as  follows  : — 

I  am  not  careful  [perhaps  this  should  be  careful  not~]  to  notice 
Professor  De  Morgan's  objections  to  the  changes  in  'Mary  Wood'  or 
*  Parley  the  Porter,'  but  would  merely  reiterate  that  the  tracts  were 
neither  designed  nor  announced  to  be  '  reprints '  of  the  originals 
[design  is  only  known  to  the  designers  ;  as  to  announcement,  the  title  is 
1  'Tis  all  for  the  best,  The  Shepherd  of  Salisbury  Plain,  and  other 
narratives,  by  Mrs.  Hannah  More ']  ;  and  much  less  [this  must  be 
careful  not;  further  removed  from  answer  than  not  careful']  can  I 
oncupy  your  space  by  a  treatise  on  the  Professor's  question :  '  May 
any  one  alter  the  works  of  the  dead  at  his  own  discretion  ? ' 

To  which  I  say — Thanks  for  help  ! 


WILLIAM   FREND'S   ALGEBRA.  117 

I  predict  that  Hannah  More's  Cheap  Repository  Tracts  will 
somewhat  resemble  the  Pilgrim's  Progress  in  their  fate.  Written 
for  the  cottage,  and  long  remaining  in  their  original  position, 
they  will  become  classical  works  of  their  kind.  Most  assuredly 
this  will  happen  if  my  assertion  cannot  be  upset,  namely — That 
they  contain  the  first  specimens  of  fiction  addressed  to  the  world 
at  large,  and  widely  circulated,  in  which  dramatic — as  distin- 
guished from  puppet — power  is  shown,  and  without  indecorum. 

According  to  some  statements  I  have  seen,  but  which  I  have 
not  verified,  other  publishing  bodies,  such  as  the  Christian 
Knowledge  Society,  have  taken  the  same  liberty  with  the  names 
of  the  dead  as  the  Eeligious  Tract  Society.  If  it  be  so,  the 
impropriety  is  the  work  of  the  smaller  spirits,  who  have  not  been 
sufficiently  overlooked.  There  must  be  an  overwhelming  majority 
in  the  higher  councils  to  feel  that,  whenever  altered  works  are 
published,  the  fact  of  alteration  should  be  made  as  prominent  as 
the  name  of  the  author.  Everything  short  of  this  is  suppression 
of  truth,  and  will  ultimately  destroy  the  credit  of  the  Society. 
Equally  necessary  is  it  that  the  alterations  should  be  noted. 
When  it  comes  to  be  known  that  the  author  before  him  is  altered, 
he  knows  not  where  nor  how  nor  by  whom,  the  lowest  reader  will 
lose  his  interest. 


The  principles  of  Algebra.     By  William  Frend.     London,  1796, 
8vo.     Second  Part,  1799. 

This  Algebra,  says  Dr.  Peacock,  shows  '  great  distrust  of  the 
results  of  algebraical  science  which  were  in  existence  at  the  time 
when  it  was  written.'  Truly  it  does ;  for,  as  Dr.  Peacock  had 
shown  by  full  citation,  it  makes  war  of  extermination  upon  all 
that  distinguishes  algebra  from  arithmetic.  Robert  Simson  and 
Baron  Maseres  were  Mr.  Frend's  predecessors  in  this  opinion. 

The  genuine  respect  which  I  entertained  for  my  father-in-law 
did  not  prevent  my  canvassing  with  perfect  freedom  his  anti- 
algebraical  and  anti-Newtonian  opinions,  in  a  long  obituary 
memoir  read  at  the  Astronomical  Society  in  February  1842, 
which  was  written  by  me.  It  was  copied  into  the  Athenceum  of 
March  19.  It  must  be  said  that  if  the  manner  in  which  algebra 
was  presented  to  the  learner  had  been  true  algebra,  he  would 
have  been  right :  and  if  he  had  confined  himself  to  protesting 
against  the  imposition  of  attraction  as  a  fundamental  part  of  the 
existence  of  matter,  he  would  have  been  in  unity  with  a  great 
many,  including  Newton  himself.  I  wish  he  had  preferred 


113  A   BUDGET   OF   PARADOXES. 

amendment  to  rejection  when  he  was  a  college   tutor  :  he  wrote 
and  spoke  English  with  a  clearness  which  is  seldom  equalled. 

His  anti-Newtonian  discussions  are  confined  to  the  preliminary 
chapters  of  his  *  Evening  Amusements,'  a  series  of  astronomical 
lessons  in  nineteen  volumes,  following  the  moon  through  a  period 
of  the  golden  numbers. 

There  is  a  mistake  about  him  which  can  never  be  destroyed. 
It  is  constantly  said  that,  at  his  celebrated  trial  in  1792,  for 
sedition  and  opposition  to  the  Liturgy,  &c.,  he  was  expelled  the 
University.  He  was  banished.  People  cannot  see  the  difference; 
but  it  made  all  the  difference  to  Mr.  Frend.  He  held  his  fellow- 
ship and  its  profits  till  his  marriage  in  1808,  and  was  a  member 
of  the  University  and  of  its  Senate  till  his  death  in  1841,  as  any 
Cambridge  Calendar  up  to  1841  will  show.  That  they  would  have 
expelled  him  if  they  could,  is  perfectly  true  ;  and  there  is  a  funny 
story — also  perfectly  true — about  their  first  proceedings  being 
under  a  statute  which  would  have  given  the  power,  had  it  not  been 
discovered  during  the  proceedings  that  the  statute  did  not  exist. 
It  had  come  so  near  to  existence  as  to  be  entered  into  the  Vice- 
Chancellor's  book  for  his  signature,  which  it  wanted,  as  was  not 
seen  till  Mr.  Frend  exposed  it :  in  fact,  the  statute  had  never 
actually  passed. 

There  is  an  absurd  mistake  in  Gunning's  '  Reminiscences  of 
Cambridge.'  In  quoting  a  passage  of  Mr.  Frend's  pamphlet, 
which  was  very  obnoxious  to  the  existing  Government,  it  is 
printed  that  the  poor  market-women  complained  that  they  were 
to  be  scotched  a  quarter  of  their  wages  by  taxation ;  and  attention 
is  called  to  the  word  by  its  being  three  times  printed  in  italics. 
In  the  pamphlet  it  is  '  sconced  ' ;  that  very  common  old  word  for 
fined  or  mulcted. 

Lord  Lyndhurst,  who  has  [1863]  just  passed  away  under  a  load 
of  years  and  honours,  was  Mr.  Frend's  private  pupil  at  Cambridge. 
At  the  time  of  the  celebrated  trial,  he  and  two  others  amused 
themselves,  and  vented  the  feeling  which  was  very  strong  among 
the  undergraduates,  by  chalking  the  walls  of  Cambridge  with 
'  Frend  for  ever!'  While  thus  engaged  in  what,  using  the  term 
legally,  we  are  probably  to  call  his  first  publication,  he  and  his 
friends  were  surprised  by  the  proctors.  Flight  and  chase  followed 
of  course:  Copley  and  one  of  the  others,  Serjeant  Rough, 
escaped  ;  the  third,  whose  name  I  forget,  but  who  afterwards,  I 
have  been  told,  was  a  bishop,1  being  lame,  was  captured  and 
impositioned.  Looking  at  the  Cambridge  Calendar  to  verify  the 

1  Herbert  Marsh,  afterwards  Bishop  of  Peterborough,  a  relation  of  my  father,  (Ed.) 


FRANCIS   PLACE— WILLIAM   COBBETT.  119 

fact  that  Copley  was  an  undergraduate  at  the  time,  I  find  that 
there  are  but  two  other  men  in  the  list  of  honours  of  his  year 
whose  names  are  now  widely  remembered.  And  they  were  both 
celebrated  schoolmasters  ;  Butler  of  Harrow,  and  Tate  of  Eichmond. 

But  Mr.  Frend  had  another  noted  pupil.  I  once  had  a  con- 
versation with  a  very  remarkable  man,  who  was  generally  called 
'  Place,  the  tailor,'  but  who  was  politician,  political  economist, 
&c.,  &c.  He  sat  in  the  room  above  his  shop — he  was  then  a 
thriving  master  tailor  at  Charing  Cross — surrounded  by  books 
enough  for  nine,  to  shame  a  proverb.  The  blue  books  alone,  cut 
up  into  strips,  would  have  measured  Great  Britain  for  oh-no-we- 
never-mention-'ems,  the  Highlands  included.  I  cannot  find  a 
biography  of  this  worthy  and  able  man.  I  happened  to  mention 
William  Frend,  and  he  said,  '  Ah !  my  old  master,  as  I  always 
call  him.  Many  and  many  a  time,  and  year  after  year,  did  he 
come  in  every  now  and  then  to  give  me  instruction,  while  I  was 
sitting  on  the  board,  working  for  my  living,  you  know.' 

Place,  who  really  was  a  sound  economist,  is  joined  with 
Cobbett,  because  they  were  together  at  one  time,  and  because  he 
was,  in  1800,  &c.,  a  great  Eadical.  But  for  Cobbett  he  had  a 
great  contempt.  He  told  me  the  following  story.  He  and  others 
were  advising  with  Cobbett  about  the  defence  he  was  to  make  on 
a  trial  for  seditious  libel  which  was  coming  on.  Said  Place,  *  You 
must  put  in  the  letters  you  have  received  from  Ministers, 
members  of  the  Commons  from  the  Speaker  downwards,  &c., 
about  your  Eegister,  and  their  wish  to  have  subjects  noted.  You 
must  then  ask  the  jury  whether  a  person  so  addressed  must  be 
considered  as  a  common  sower  of  sedition,  &c.  You  will  be 
acquitted ;  nay,  if  your  intention  should  get  about,  veiy  likely 
they  will  manage  to  stop  proceedings.'  Cobbett  was  too  much 

disturbed  to  listen  ;  he  walked  about  the  room  ejaculating  '  D 

the  prison  ! '  and  the  like.  He  had  not  the  sense  to  follow  the 
advice,  and  was  convicted. 

Cobbett,  to  go  on  with  the  chain,  was  a  political  acrobat,  ready 
for  any  kind  of  posture.  A  friend  of  mine  gave  me  several  times 
an  account  of  a  mission  to  him.  A  Tory  member — those  who 
know  the  old  Tory  world  may  look  for  his  initials  in  initials  of 
two  consecutive  words  of  '  Pay  his  money  with  interest ' — who 
was,  of  course,  a  political  opponent,  thought  Cobbett  had  been 
hardly  used,  and  determined  to  subscribe  handsomely  towards  the 
expenses  he  was  incurring  as  a  candidate.  My  friend  was  com- 
missioned to  hand  over  the  money — a  bag  of  sovereigns,  that  notes 
might  not  be  traced.  He  went  into  Cobbett's  committee-room, 


120  A   BUDGET   OF  PARADOXES. 

told  the  patriot  his  errand,  and  put  the  money  on  the  table. 
'  And  to  whom,  sir,  am  I  indebted  ? '  said  Cobbett.  '  The  donor,' 
was  the  answer,  '  is  Mr.  Andrew  Theophilus  Smith,'  or  some  such 
unlikely  pair  of  baptismals.  '  Ah ! '  said  Cobbett,  '  I  have  known  Mr. 
A.  T.  S.  a  long  time !  he  was  always  a  true  friend  of  his  country  1 ' 
To  return  to  Place.  He  is  a  noted  instance  of  the  advantage 
of  our  jury  system,  which  never  asks  a  man's  politics,  &c.  The 
late  King  of  Hanover,  when  Duke  of  Cumberland,  being  unpopular, 
was  brought  under  unjust  suspicions  by  the  suicide  of  his  valet : 
he  must  have  seduced  the  wife  and  murdered  the  husband.  The 
charges  were  as  absurd  as  those  brought  against  the  Englishman 
in  the  Frenchman's  attempt  at  satirical  verses  upon  him  : — 

The  Englishman  is  a  very  bad  man  ; 
He  drink  the  beer  and  lie  steal  the  can  : 
He  kiss  the  wife  and  he  beat  the  man  ; 
And  the  Englishman  is  a  very  G d . 


The  charges  were  revived  in  a  much  later  day,  and  the  defence 
might  have  given  some  trouble.  But  Place,  who  had  been  the 
foreman  at  the  inquest,  came  forward,  and  settled  the  question  in 
a  few  lines.  Everyone  knew  that  the  old  Radical  was  quite  free 
of  all  disposition  to  suppress  truth  from  wish  to  curry  favour  with 
royalty. 

John  Speed,  the  author  of  the  English  History  (1632)  which 
Bishop  Nicolson  calls  the  best  chronicle  extant,  was  a  man,  like 
Place,  of  no  education  but  what  he  gave  himself.  The  bishop 
says  he  would  have  done  better  if  he  had  had  better  training : 
but  what,  he  adds,  could  have  been  expected  from  a  tailor  !  This 
Speed  was,  as  well  as  Place.  But  he  was  released  from  manual 
labour  by  Sir  Fulk  Grevil,  who  enabled  him  to  study. 

I  have  elsewhere  noticed  that  those  who  oppose  the  mysteries 
of  algebra  do  not  ridicule  them ;  this  I  want  the  cyclometers  to 
do.  Of  the  three  who  wrote  against  the  great  point,  the  negative 
quantity,  and  the  uses  of  0  which  are  connected  with  it,  only 
one  could  fire  a  squib.  That  Robert  Simson  should  do  such  a 
thing  will  be  judged  impossible  by  all  who  admit  tradition.  I 
do  not  vouch  for  the  following  ;  I  give  it  as  a  proof  of  the 
impression  which  prevailed  about  him : — 

He  used  to  sit  at  his  open  window  on  the  ground  floor,  as  deep 
in  geometry  as  a  Robert  Simson  ought  to  be.  Here  he  would  be 
accosted  by  beggars,  to  whom  he  generally  gave  a  trifle ,  he 
roused  himself  to  hear  a  few  words  of  the  story,  made  his  dona- 
tion, and  instantly  dropped  down  into  his  depths.  Some  wags 


MASERES   ON   THE   NEGATIVE   SIGN.  121 

one  day  stopped  a  mendicant  who  was  on  his  way  to  the  window, 
with  '  Now,  my  man,  do  as  we  tell  you,  and  you  will  get  some- 
thing from  that  gentleman,  and  a  shilling  from  us  besides.  You 
will  go  and  say  you  are  in  distress,  he  will  ask  you  who  you  are, 
and  you  will  say  you  are  Robert  Simson,  son  of  John  Simson  of 
Kirktonhill.'  The  man  did  as  he  was  told  ;  Simson  quietly  gave 
him  a  coin,  and  dropped  off.  The  wags  watched  a  little,  and  saw 
him  rouse  himself  again,  and  exclaim  '  Robert  Simson,  son  of 
John  Simson  of  Kirktonhill !  why,  that  is  myself.  That  man 
must  be  an  impostor.'  Lord  Brougham  tells  the  same  story,  with 
some  difference  of  details. 

Baron  Maseres  was,  as  a  writer,  dry ;  those  who  know  his 
writings  will  feel  that  he  seldom  could  have  taken  in  a  joke  or 
issued  a  pun.  Maseres  was  the  fourth  wrangler  of  1752,  and 
first  Chancellor's  medallist  (or  highest  in  classics) ;  his  second 
was  Porteus  (afterwards  Bishop  of  London).  Waring  came  five 
years  after  him :  he  could  not  get  Maseres  through  the  second 
page  of  his  first  work  on  algebra ;  a  negative  quantity  stood 
like  a  lion  in  the  way.  In  1758  he  published  his 'Dissertation 
on  the  Use  of  the  Negative  Sign,'  4to.  There  are  some  who  care 
little  about  -f-  and  — ,  who  would  give  it  house-room  for  the  sake 
of  the  four  words  '  Printed  by  Samuel  Richardson.' 

Maseres  speaks  as  follows :  '  A  single  quantity  can  never  be 
marked  with  either  of  those  signs,  or  considered  as  either  affirma- 
tive or  negative ;  for  if  any  single  quantity,  as  6,  is  marked 
either  with  the  sign  -f-  or  with  the  sign  —  without  assigning 
some  other  quantity,  as  a,  to  which  it  is  to  be  added,  or  from 
which  it  is  to  be  subtracted,  the  mark  will  have  no  meaning  or 
signification :  thus  if  it  be  said  that  the  square  of  —  5,  or  the 
product  of  — 5  into  —5,  is  equal  to  +25,  such  an  assertion  must 
either  signify  no  more  than  that  5  times  5  is  equal  to  25  without 
any  regard  to  the  signs,  or  it  must  be  mere  nonsense  and  unin- 
telligible jargon.  I  speak  according  to  the  foregoing  definition, 
by  which  the  affirmativeness  or  negativeness  of  any  quantity 
implies  a  relation  to  another  quantity  of  the  same  kind  to  which 
it  is  added,  or  from  which  it  is  subtracted ;  for  it  may  perhaps  be 
very  clear  and  intelligible  to  those  who  have  formed  to  them- 
selves some  other  idea  of  affirmative  and  negative  quantities 
different  from  that  above  defined.' 

Nothing  can  be  more  correct,  or  more  identically  logical :  +  5 
and  — 5,  standing  alone,  are  jargon  if  +5  and  — 5  are  to  be 
understood  as  without  reference  to  another  quantity.  But  those 
who  have  '  formed  to  themselves  some  other  idea '  see  meaning 


122  A   BUDGET   OF  PARADOXES. 

enough.  The  great  difficulty  of  the  opponents  of  algebra  lay  in 
want  of  power  or  will  to  see  extension  of  terms.  Maseres  is  right 
when  he  implies  that  extension,  accompanied  by  its  refusal, 
makes  jargon.  One  of  my  paradoxers  was  present  at  a  meeting 
of  the  Koyal  Society  (in  1864,  I  think)  and  asked  permis- 
sion to  make  some  remarks  upon  a  paper.  He  rambled  into 
other  things,  and,  naming  me,  said  that  I  had  written  a 
book  in  which  two  sides  of  a  triangle  are  pronounced  equal  to 
the  third.  So  they  are,  in  the  sense  in  which  the  word  is  used 
in  complete  algebra;  in  which  A  +  B  =  C  makes  A,  B,  c,  three 
sides  of  a  triangle,  and  declares  that  going  over  A  and  B,  one  after 
the  other,  is  equivalent,  in  change  of  place,  to  going  over  c  at 
once.  My  critic,  who  might,  if  he  pleased,  have  objected  to 
extension,  insisted  upon  reading  me  in  unextended  meaning. 

On  the  other  hand,  it  must  be  said  that  those  who  wrote  on 
the  other  idea  wrote  very  obscurely  about  it,  and  justified  Des 
Cartes  (De  Methodo]  when  he  said :  '  Algebram  vero,  ut  solet 
doceri,  animadverti  certis  regulis  et  numerandi  formulis  ita  esse 
contentam,  ut  videatur  potius  ars  qua3dam  confusa,  cujus  usu 
ingenium  quodam  modo  turbatur  et  obscuratur,  quam  scientia 
qua  excolatur  et  perspicacius  reddatur.'  Maseres  wrote  this 
sentence  on  the  title  of  his  own  copy  of  his  own  work,  now  before 
me  ;  he  would  have  made  it  his  motto  if  he  had  found  it  earlier. 
There  is,  I  believe,  in  Cobbett's  '  Annual  Kegister,'  an  account 
of  an  interview  between  Maseres  and  Cobbett  when  in  prison. 

The  conversation  of  Maseres  was  lively,  and  full  of  serious  anec- 
dote :  but  only  one  attempt  at  humorous  satire  is  recorded  of 
him;  it  is  an  instructive  one.  He  was  born  in  1731  (Dec.  15), 
and  his  father  was  a  refugee.  P'rench  was  the  language  of  the 
house,  with  the  pronunciation  of  the  time  of  Louis  XIV.  He 
lived  until  1824  (May  19),  and  saw  the  race  of  refugees  who 
were  driven  out  by  the  first  Eevolution.  Their  pronunciation 
differed  greatly  from  his  own ;  and  he  used  to  amuse  himself  by 
mimicking  them.  Those  who  heard  him  and  them  had  the  two 
schools  of  pronunciation  before  them  at  once;  a  thing  which 
seldom  happens.  It  might  even  yet  be  worth  while  to  examine 
the  Canadian  pronunciation. 

Maseres  went  as  Attorney-General  to  Quebec;  and  was  ap- 
pointed Cursitor  Baron  of  our  Exchequer  in  1773.  There  is  a 
curious  story  about  his  mission  to  Canada,  which  I  have  heard  as 
good  tradition,  but  have  never  seen  in  print.  The  reader  shall 
have  it  as  cheap  as  I ;  and  I  confess  I  rather  believe  it.  Maseres 
was  inveterately  honest ;  he  could  not,  at  the  bar,  boar  to  see  his 


BARON   MASERES.  123 

own  client  victorious,  when  be  knew  his  cause  was  a  bad  one. 
On  a  certain  occasion  he  was  in  a  cause  which  he  knew  would 
go  against  him  if  a  certain  case  were  quoted.  Neither  the  judge 
nor  the  opposite  counsel  seemed  to  remember  this  case,  and 
Ma  seres  could  not  help  dropping  an  allusion  which  brought  it 
out.  His  business  as  a  barrister  fell  off,  of  course.  Some  time 
after,  Mr.  Pitt  (Chatham)  wanted  a  lawyer  to  send  to  Canada  on 
a  private  mission,  and  wanted  a  very  honest  man.  Some  one 
mentioned  Maseres,  and  told  the  above  story :  Pitt  saw  that  he 
had  got  the  man  he  wanted.  The  mission  was  satisfactorily  per- 
formed, and  Maseres  remained  as  Attorney-General. 

The  'Doctrine  of  Life  Annuities'  (4to.  726  pages,  1783)  is  a 
strange  paradox.  Its  size,  the  heavy  dissertations  on  the  national 
debt,  and  the  depth  of  algebra  supposed  known,  put  it  out  of 
the  question  as  an  elementary  work,  and  it  is  unfitted  for  the 
higher  student  by  its  elaborate  attempt  at  elementary  character, 
shown  in  its  rejection  of  forms  derived  from  chances  in  favour  of 
the  average,  and  its  exhibition  of  the  separate  values  of  the 
years  of  an  annuity,  as  arithmetical  illustrations.  It  is  a  climax 
of  unsaleability,  unreadability,  and  inutility.  For  intrinsic 
nullity  of  interest,  and  dilution  of  little  matter  with  much  ink, 
I  can  compare  this  book  to  nothing  but  that  of  Claude  de  St. 
Martin,  elsewhere  mentioned,  or  the  lectures  *  On  the  Nature  and 
Properties  of  Logarithms,'  by  James  Little,  Dublin,  1830,  8vo. 
(254  heavy  pages  of  many  words  and  few  symbols),  a  wonderful 
weight  of  weariness. 

The  stock  of  this  work  on  annuities,  very  little  diminished, 
was  given  by  the  author  to  William  Frend,  who  paid  warehouse 
room  for  it  until  about  1835,  when  he  consulted  me  as  to  its 
disposal.  As  no  publisher  could  be  found  who  would  take  it 
as  a  gift,  for  any  purpose  of  sale,  it  was  consigned,  all  but  a  few 
copies,  to  a  buyer  of  waste  paper. 

Baron  Maseres's  republications  are  well  known :  the  Scriptona 
Logarithmici  is  a  set  of  valuable  reprints,  mixed  with  much 
which  might  better  have  entered  into  another  collection.  It  is 
not  so  well  known  that .  there  is  a  volume  of  optical  reprints, 
Sci^iptores  Optici,  London,  1823,  4to,  edited  for  the  veteran  of 
ninety-two  by  Mr.  Babbage  at  twenty-nine.  This  excellent 
volume  contains  James  Gregory,  Des  Cartes,  Halley,  Barrow, 
and  the  optical  writings  of  Huyghens,  the  Principia  of  the 
undulatory  theory.  It  also  contains,  by  the  sort  of  whim  in 
which  such  men  as  Maseres,  myself,  and  some  others  are  apt 
to  indulge,  a  reprint  of  '  The  great  and  new  Art  of  weighing 


124  A   BUDGET   OF  PARADOXES. 

Vanity,'  by  M.  Patrick  Mathers,  Arch-Bedel  to  the  University  of 
St.  Andrews,  Glasgow,  1672.  Professor  Sinclair,  of  Glasgow,  a 
good  man  at  clearing  mines  of  the  water  which  they  did  not 
want,  and  furnishing  cities  with  the  water  which  they  did  want, 
seems  to  have  written  absurdly  about  hydrostatics,  and  to  have 
attacked  a  certain  Sanders,  M.A.  So  Sanders,  assisted  by  James 
Gregory,  published  a  heavy  bit  of  jocosity  about  him.  This 
story  of  the  authorship  rested  on  a  note  made  in  his  copy 
by  Kobert  Gray,  M.D. ;  but  it  has  since  been  fully  confirmed  by 
a  letter  of  James  Gregory  to  Collins,  in  the  Macclesfield  Corre- 
spondence. '  There  is  one  Master  Sinclair,  who  did  write  the 
Ars  Magna  et  Nova,  a  pitiful  ignorant  fellow,  who  hath  lately 
written  horrid  nonsense  in  the  hydrostatics,  and  hath  abused  a 
master  in  the  University,  one  Mr.  Sanders,  in  print.  This  Mr. 
Sanders  ...  is  resolved  to  cause  the  Bedel  of  the  University 
to  write  against  him.  .  .  .  We  resolve  to  make  excellent  sport 
with  him.' 

On  this  I  make  two  remarks  :  First,  I  have  learnt  from  ex- 
perience that  old  notes,  made  in  books  by  their  possessors,  are 
statements  of  high  authority :  they  are  almost  always  confirmed. 
I  do  not  receive  them  without  hesitation  ;  but  I  believe  that 
of  all  the  statements  about  books  which  rest  on  one  authority, 
there  is  a  larger  percentage  of  truth  in  the  written  word  than  in 
the  printed  word.  Secondly,  I  mourn  to  think  that  when  the 
New  /Jealander  picks  up  his  old  copy  of  this  book,  and  reads  it 
by  the  associations  of  his  own  day,  he  may,  in  spite  of  the  many 
assurances  I  have  received  that  my  Athenceum  Budget  was 
amusing,  feel  me  to  be  as  heavy  as  I  feel  James  Gregory  and 
Sanders.  But  he  will  see  that  I  knew  what  was  coming,  which 
Gregory  did  not. 

It  was  left  for  William  Frend  to  prove  that  an  impugner  ol 
algebra  could  attempt  ridicule.  He  was,  in  1803,  editor  of  a 
periodical  The  Gentleman's  Monthly  Miscellany,  which  lasted 
a  few  months.  To  this,  among  other  things,  he  contributed  the 
following,  in  burlesque  of  the  use  made  of  0,  to  which  he  ob- 
jected. The  imitation  of  Eabelais,  a  writer  in  whom  he  de- 
lighted, is  good  :  to  those  who  have  never  dipped,  it  may  give 
such  a  notion  as  they  would  not  easily  get  elsewhere.  The  point 
of  the  satire  is  not  so  good.  But  in  truth  it  is  not  easy  to  make 
pungent  scoffs  upon  what  is  common  sense  to  all  mankind.  Who 
can  laugh  with  effect  at  six  times  nothing  is  nothing,  as  false  or 
unintelligible?  In  an  article  intended  for  that  undistinguishing 
know-0  the  '  general  reader,'  there  would  have  been  no  force  of 


IMITATION   OF  RABELAIS.  125 

satire,  if  division  by  0  had  been  separated  from  multiplication 
by  the  same. 

I  have  followed  the  above  by  another  squib,  by  the  same 
author,  on  the  English  language.  The  satire  is  covertly  aimed  at 
theological  phraseology;  and  any  one  who  watches  this  subject 
will  see  that  it  is  a  very  just  observation  that  the  Greek  words 
are  not  boiled  enough. 


PANTAGRUEL'S  DECISION  of  the  QUESTION  about  NOTHING. 

PANTAGRUEL  determined  to  Lave  a  snug  afternoon  with  Epistemon  and 
Panurge.  Dinner  was  ordered  to  be  set  in  a  small  parlour,  and  a 
particular  batch  of  Hermitage  with  some  choice  Burgundy  to  be  drawn 
from  a  remote  corner  of  the  cellar  upon  the  occasion.  By  way  of 
lunch,  about  an  hour  before  dinner,  Pantagruel  was  composing  his 
stomach  with  German  sausages,  reindeer's  tongues,  oysters,  brawn,  and 
half  a  dozen  different  sorts  of  English  beer  just  come  into  fashion,  when 
a  most  thundering  knocking  was  heard  at  the  great  gate,  and  from  the 
noise  they  expected  it  to  announce  the  arrival  at  least  of  the  First 
Consul,  or  king  Gargantua.  Panurge  was  sent  to  reconnoitre,  and 
after  a  quarter  of  an  hoar's  absence,  returned  with  the  news  that  the 
University  of  Pontemaca  was  waiting  his  highness's  leisure  in  the 
great  hall,  to  propound  a  question  which  had  turned  the  brains  of 
thirty-nine  students,  and  had  flung  twenty-seven  more  into  a  high 
fever.  With  all  my  heart,  says  Pantagruel,  and  swallowed  down  three 
quarts  of  Burton  ale  ;  but  remember,  it  wants  but  an  hour  of  dinner 
time,  and  the  question  must  be  asked  in  as  few  words  as  possible  ;  for 
I  cannot  deprive  myself  of  the  pleasure  I  expected  to  enjoy  in  the 
company  of  my  good  friends  for  a  set  of  mad-headed  masters.  I  wish 
brother  John  was  here  to  settle  these  matters  with  the  black  gentry. 

Having  said  or  rather  growled  this,  he  proceeded  to  the  hall  of 
ceremony,  and  mounted  his  throne  ;  Epistemon  and  Panurge  standing 
on  each  side,  but  two  steps  below  him.  Then  advanced  to  the  throne 
the  three  beadles  of  the  University  of  Pontemaca  with  their  silver 
staves  on  their  shoulders,  and  velvet  caps  on  their  heads,  and  they 
were  followed  by  three  times  three  doctors,  and  thrice  three  times 
three  masters  of  art ;  for  everything  was  done  in  Pontemaca  by  the 
number  three,  and  on  this  account  the  address  was  written  on  parch- 
ment, one  foot  in  breadth,  and  thrice  three  times  thrice  three  feet  in 
length.  The  beadles  struck  the  ground  with  their  heads  and  their 
staves  three  times  in  approaching  the  throne  ;  the  doctors  struck  the 
ground  with  their  heads  thrice  three  times,  and  the  masters  did  the 
same  thrice  each  time,  beating  the  ground  with  their  heads  thrico 
three  times.  This  was  the  accustomed  form  of  approaching  the  throne, 
time  out  of  mind,  and  it  was  said  to  be  emblematic  of  the  usual  pios- 
tration  of  science  to  the  throne  of  greatness. 


12G  A  BUDGET   OF  PAKADOXES. 

The  mathematical  professor,  after  having  spit,  and  hawked,  and 
cleared  his  throat,  and  hlown  his  nose  on  a  handkerchief  lent  to  him, 
for  he  had  forgotten  to  bring  his  own,  began  to  read  the  address.  In 
this  he  was  assisted  by  three  masters  of  arts,  one  of  whom,  with  a 
silver  pen,  pointed  out  the  stops ;  the  second  with  a  small  stick  rapped 
his  knuckles  when  he  was  to  raise  or  lower  his  voice ;  and  a  third 
pulled  his  hair  behind  when  he  was  to  look  Pantagruel  in  the  face. 
Pantagruel  began  to  chafe  like  a  lion  :  he  turned  first  on  one  side,  then 
on  the  other  :  he  listened  and  groaned,  and  groaned  and  listened,  and 
was  in  the  utmost  cogitabundity  of  cogitation.  His  countenance 
began  to  brighten,  when,  at  the  end  of  an  hour,  the  reader  stammered 
out  these  words : 

'  It  has  therefore  been  most  clearly  proved,  that  as  all  matter  may 
be  divided  into  parts  infinitely  smaller  than  the  infinitely  smallest  part 
of  the  infinitesimal  of  nothing,  so  nothing  has  all  the  properties  of 
something,  and  may  become,  by  just  and  lawful  right,  susceptible  of 
addition,  subtraction,  multiplication,  division,  squaring,  and  cubing  : 
that  it  is  to  all  intents  and  purposes  as  good  as  anything  that  has 
been,  is,  or  can  be  taught  in  the  nine  universities  of  the  land,  and  to 
deprive  it  of  its  rights  is  a  most  cruel  innovation  and  usurpation, 
tending  to  destroy  all  just  subordination  in  the  world,  making  all 
universities  superfluous,  levelling  vice-chancellors,  doctors,  and  proctors, 
masters,  bachelors,  and  scholars,  to  the  mean  and  contemptible  state  of 
butchers  and  tallow-chandlers,  bricklayers  and  chimney-sweepers,  who, 
if  it  were  pot  for  these  learned  mysteries,  might  think  that  they  knew 
as  much  as"  their  betters.  Every  one  then,  who  has  the  good  of  science 
at  heart,  must  pray  for  the  interference  of  his  highness  to  put  a  stop 
to  all  the  disputes  about  nothing,  and  by  his  decision  to  convince  all 
gainsayers  that  the  science  of  nothing  is  taught  in  the  best  manner  in 
the  universities,  to  the  great  edification  and  improvement  of  all  the 
youth  in  the  land.' 

Here  Pantagruel  whispered  in  the  ear  of  Panurge,  who  nodded  to 
Epistemon,  and  they  two  left  the  assembly,  and  did  not  return  for  an 
hour,  till  the  orator  had  finished  his  task.  The  three  beadles  had 
thrice  struck  the  ground  with  their  heads  and  staves,  the  doctors  had 
finished  their  compliments,  and  the  masters  Were  making  their  twenty- 
seven  prostrations.  Epistemon  and  Panurge  went  up  to  Pantagruel, 
whom  they  found  fast  asleep  and  snoring ;  nor  could  he  be  roused  but 
by  as  many  tugs  as  there  had  been  bowings  from  the  corps  of  learning. 
At  last  he  opened  his  eyes,  gave  a  good  stretch,  made  half  a  dozen 
yawns,  and  called  for  a  stoup  of  wine.  I  thank  you,  my  masters,  says 
be ;  so  sound  a  nap  I  have  not  had  since  I  came  from '  the  island  of 
Priestfolly.  Have  you  dined,  my  masters  ?  They  answered  the 
question  by  as  many  bows  as  at  entrance  ;  but  his  highness  left  them 
to  the  care  of  Panurge,  and  retired  to  the  little  parlour  with  Epistemon, 
where  they  burst  into  a  fit  of  laughter,  declaring  that  this  learned 
Buragouin  about  nothing  was  just  as  intelligible  as  the  lawyer's 


IMITATION   OF   RABELAIS.  127 

Galimathias.  Panurge  conducted  the  learned  body  into  a  large  saloon, 
and  each  in  his  way  hearing  a  clattering  of  plates  and  glasses,  con- 
gratulated himself  on  his  approaching  good  cheer.  There  they  wero 
left  by  Panurge,  who  took  his  chair  by  Pantagrnel  just  as  the  spup 
was  removed,  but  he  made  up  for  the  want  of  that  part  of  his  dinner 
by  a  pint  of  Champagne.  The  learning  of  the  university  had  whetted 
their  appetites  ;  what  they  each  ate  it  is  needless  to  recite  ;  good  wine, 
good  stories,  and  hearty  laughs  went  round,  and  three  hours  elapsed 
before  one  soul  of  them  recollected  the  hungry  students  of  Pontemaca. 

Epistemon  reminded  them  of  the  business  in  hand,  and  orders  were 
given  for  a  fresh  dozen  of  hermitage  to  be  put  upon  table,  and  the 
royal  attendants  to  get  ready.  As  soon  as  the  dozen  bottles  were 
emptied,  Pantagruel  rose  from  table,  the  royal  trumpets  sounded,  and 
he  was  accompanied  by  the  great  officers  of  his  court  into  the  large 
dining  hall,  where  was  a  table  with  forty-two  covers.  Pantagruel  sat 
at  the  head,  Epistemon  at  the  bottom,  and  Panurge  in  the  middle, 
opposite  an  immense  silver  tureen,  which  would  hold  fifty  gallons  of 
soup.  The  wise  men  of  Pontemaca  then  took  their  scats  according  to 
seniority.  Every  countenance  glistened  with  delight ;  the  music  struck 
up  ;  the  dishes  were  uncovered.  Panurge  had  enough  to  do  to  handle 
the  immense  silver  ladle  :  Pantagruel  and  Epistemon  had  no  time  for 
eating,  they  were  fully  employed  in  carving.  The  bill  of  fare  announced 
the  names  of  a  hundred  different  dishes.  From  Panurge's  ladle  came 
into  the  soup  plate  as  much  as  he  took  every  time  out  of  the  tureen ; 
and  as  it  was  the  rule  of  the  court  that  every  one  should  appear  to  eat, 
as  long  as  he  sat  at  table,  there  was  the  clattering  of  nine  and  thirty 
spoons  against  the  silver  soup-plates  for  a  quarter  of  an  hour.  They 
were  then  removed,  and  knives  and  forks  were  in  motion  for  half  an 
hour.  Glasses  were  continually  handed  round  in  the  mean  time,  and 
then  everything  was  removed,  except  the  great  tureen  of  soup.  The 
second  course  was  now  served  up,  in  dispatching  which  half  an  hour 
was  consumed ;  and  at  the  conclusion  the  wise  men  of  Pontemaca  had 
just  as  much  in  their  stomachs  as  Pantagruel  in  his  head  from  their 
address :  for  nothing  was  cooked  up  for  them  in  every  possible  shape 
that  Panurge  could  devise. 

Wine-glasses,  large  decanters,  fruit  dishes,  and  plates  were  now  set 
on.  Pantagruel  and  Epistemon  alternately  gave  bumper  toasts :  the 
University  of  Pontemaca,  the  eye  of  the  world,  the  mother  of  taste  and 
good  sense  and  universal  learning,  the  patroness  of  utility,  and  the 
second  only  to  Pantagruel  in  wisdom  and  virtue  (for  these  were  her 
titles),  was  drank  standing  with  thrice  three  times  three,  and  huzzas 
and  clatterings  of  glasses  ;  but  to  such  wine  the  wise  men  of  Pontemaca 
had  not  been  accustomed  ;  and  though  Pantagruel  did  not  suffer  one 
to  rise  from  table  till  the  eighty-first  glass  had  been  emptied,  not  even 
the  weakest  headed  master  of  arts  felt  his  head  in  the  least  indisposed. 
The  decanters  indeed  were  often  removed,  but  they  were  brought  back 
replenished,  filled  always  with  nothing. 


128  A  BUDGET  OF  PAKADOXES. 

Silence  was  now  proclaimed,  and  in  a  trice  Panurge  leaped  into  the 
large  silver  tureen.  Thence  he  made  his  bows  to  Pantagruel  and  the 
whole  company,  and  commenced  an  oration  of  signs,  which  lasted  au. 
hour  and  a  half,  and  in  which  he  went  over  all  the  matter  contained 
in  the  Pontemacan  address ;  and  though  the  wise  men  looked  very 
serious  during  the  whole  time,  Pantagruel  himself  and  his  whole  court 
could  not  help  indulging  in  repeated  bursts  of  laughter.  It  was 
universally  acknowledged  that  he  excelled  himself,  and  that  the  ar- 
guments by  which  he  beat  the  English  masters  of  arts  at  Paris  were 
nothing  to  the  exquisite  selection  of  attitudes  which  he  this  day 
assumed.  The  greatest  shouts  of  applause  were  excited  when  he  was 
running  thrice  round  the  tureen  on  its  rim,  with  his  left  hand  holding 
his  nose,  and  the  other  exercising  itself  nine  and  thirty  times  on  his 
back.  In  this  attitude  he  concluded  with  his  back  to  the  pro- 
fessor of  mathematics  ;  and  at  the  instant  he  gave  his  last  flap,  by  a 
sudden  jump,  and  turning  heels  over  head  in  the  air,  he  presented 
himself  face  to  face  to  the  professor,  and  standing  on  his  left  leg,  with 
his  left  hand  holding  his  nose,  he  presented  to  him,  in  a  white  satin 
bag,  Pantagruel's  royal  decree.  Then  advancing  his  right  leg,  he 
fixed  it  on  the  professor's  head,  and  after  three  turns,  in  which  he 
clapped  his  sides  with  both  hands  thrice  three  times,  down  he 
leaped,  and  Pantagruel,  Epistemon,  and  himself  took  their  leaves  of  the 
wise  men  of  Pontemaca. 

The  wise  men  now  retired,  and  by  royal  orders  were  accompanied 
by  a  guard,  and  according  to  the  etiquette  of  the  court,  no  one  having 
a  royal  order  could  stop  at  any  public  house  till  it  was  delivered.  The 
procession  arrived  at  Pontemaca  at  nine  o'clock  the  next  morning,  and 
the  sound  of  bells  from  every  church  and  college  announced  their 
arrival.  The  congregation  was  assembled ;  the  royal  decree  was 
saluted  in  the  same  manner  as  if  his  highness  had  been  there  in 
person ;  and  after  the  proper  ceremonies  had  been  performed,  the 
satin  bag  was  opened  exactly  at  twelve  o'clock.  A  finely  emblazoned 
roll  was  drawn  forth,  and  the  public  orator  read  to  the  gaping  assembly 
the  following  words  : 

'  They  who  can  make  something  out  of  nothing  shall  have  nothing 
to  eat  at  the  court  of — PANTAGKUEL.' 


ORIGIN  of  the  ENGLISH  LANGUAGE,  related  ly  a  SWEDE. 

SOME  months  ago  in  a  party  in  Holland,  consisting  of  natives  of  various 
countries,  the  merit  of  their  respective  languages  became  a  topic  of 
conversation.  A  Swede,  who  had  been  a  great  traveller,  and  could 
converse  in  most  of  the  modern  languages  of  Europe,  laughed  very 
heartily  at  an  Englishman,  who  had  ventured  to  speak  in  praise  of  the 
tongue  of  his  dear  country.  I  never  had  any  trouble,  says  he,  in  learning 
English.  To  my  very  great  surprise,  the  moment  I  sat  foot  on  shore 


ORIGIN  OF  ENGLISH;  A  FABLE.  129 

at  Gravesend,  I  found  out,  that  I  could  understand,  with  very  little 
trouble,  every  word  that  was  said.  It  was  a  mere  jargon,  made  up  of 
German,  French,  and  Italian,  with  now  and  then  a  word  from  the 
Spanish,  Latin,  or  Greek.  I  had  only  to  bring  my  mouth  to  their 
mode  of  speaking,  which  was  done  with  ease  in  less  than  a  week,  and 
I  was  every  where  taken  for  a  true-born  Englishman ;  a  privilege  by 
the  way  of  no  small  importance  in  a  country,  where  each  man,  God 
knows  why,  thinks  his  foggy  island  superior  to  any  other  part  of  the 
world :  and  though  his  door  is  never  free  from  some  dun  or  other 
coming  for  a  tax,  and  if  he  steps  out  of  it  he  is  sure  to  be  knocked 
down  or  to  have  his  pocket  picked,  yet  he  has  the  insolence  to  think 
every  foreigner  a  miserable  slave,  and  his  country  the  seat  of  every 
thing  wretched.  They  may  talk  of  liberty  as  they  please,  but  Spain 
or  Turkey  for  my  money :  barring  the  bowstring  and  the  inquisition, 
they  are  the  most  comfortable  countries  under  heaven,  and  you  need 
not  be  afraid  of  either,  if  you  do  not  talk  of  religion  and  politics.  I  do 
not  see  much  difference  too  in  this  respect  in  England,  for  when  I  was 
there,  one  of  their  most  eminent  men  for  learning  was  put  in  prison 
for  a  couple  of  years,  and  got  his  death  for  translating  one  of  j9Ssop's 
fables  into  English,  which  every  child  in  Spain  and  Turkey  is  taught, 
as  soon  as  he  comes  out  of  his  leading  strings.  Here  all  the  company 
unanimously  cried  out  against  the  Swede,  that  it  was  impossible  :  for  in 
England,  the  land  of  liberty,  the  only  thing  its  worst  enemies  could 
pay  against  it,  was,  that  they  paid  for  their  liberty  a  much  greater 
price  than  it  was  worth. — Every  man  there  had  a  fair  trial  accord- 
ing to  laws,  which  every  body  could  understand  ;  and  the  judges  were 
cool,  patient,  discerning  men,  who  never  took  the  part  of  the  crown 
against  the  prisoner,  but  gave  him  every  assistance  possible  for  his 
defence. 

The  Swede  was  borne  down,  but  not  convinced ;  and  he  seemed 
determined  to  spit  out  all  his  venom.  Well,  says  he,  at  any  rate  you 
will  not  deny  that  the  English  have  not  got  a  language  of  their  own, 
and  that  they  came  by  it  in  a  very  odd  way.  Of  this  at  least  I  am 
certain,  for  the  whole  history  was  related  to  me  by  a  witch  in  Lapland, 
whilst  I  was  bargaining  for  a  wind.  Here  the  company  were  all  in 
unison  again  for  the  story. 

In  antient  times,  said  the  old  hag,  the  English  occupied  a  spot  in 
Tartary,  where  they  lived  sulkily  by  themselves,  unknowing  and  un- 
known. By  a  great  convulsion  that  took  place  in  China,  the  inhabit- 
ants of  that  and  the  adjoining  parts  of  Tartary  were  driven  from  their 
seats,  and  after  various  wanderings  took  up  their  abode  in  Germany. 
During  this  time  no  body  could  understand  the  English,  for  they  did 
not  talk,  but  hissed  like  so  many  snakes.  The  poor  people  felt  uneasy 
under  this  circumstance,  and  in  one  of  their  parliaments,  or  rather 
hissing  meetings,  it  was  determined  to  seek  for  a  remedy :  and  an 
embassy  was  sent  to  some  of  our  sisterhood  then  living  on  Mount 
Hccla.  They  were  put  to  a  nonplus,  and  summoned  the  Devil  to  their 

K 


130  A  BUDGET    OF   PAEADOXE8. 

relief.  To  him  the  English  presented  their  petitions,  and  explained 
their  sad  case  ;  and  he,  upon  certain  conditions,  promised  to  befriend 
them,  and  to  give  them  a  language.  The  poor  Devil  was  little  aware 
of  what  he  had  promised  ;  but  he  is,  as  all  the  world  knows,  a  man  of 
too  much  honour  to  break  his  word.  Up  and  down  the  world  then  he 
went  in  quest  of  this  new  language  :  visited  all  the  universities,  and 
all  the  schools,  and  all  the  courts  of  law,  and  all  the  play-houses,  and 
all  the  prisons ;  never  was  poor  devil  so  fagged.  It  would  have  made 
your  heart  bleed  to  see  him.  Thrice  did  he  go  round  the  earth  in 
every  parallel  of  latitude ;  and  at  last,  wearied  and  jaded  out,  back 
came  he  to  Hecla  in  despair,  and  would  have  thrown  himself  into  the 
volcano,  if  he  had  been  made  of  combustible  materials.  Luckily  at 
that  time  our  sisters  were  engaged  in  settling  the  balance  of  Europe ; 
and  whilst  they  were  looking  over  projects,  and  counter-projects,  and 
ultimatums,  and  post  ultimatums,  the  poor  Devil,  unable  to  assist  them, 
was  groaning  in  a  corner  and  ruminating  over  his  sad  condition. 

On  a  sudden,  a  hellish  joy  overspread  his  countenance;  up  he 
jumped,  and,  like  Archimedes  of  old,  ran  like  a  madman  amongst  the 
thi-ong,  turning  over  tables,  and  papers,  and  witches,  roaring  out  for  a 
full  hour  together  nothing  else  but  'tis  found,  'tis  found  !  Away  were 
sent  the  sisterhood  in  every  direction,  some  to  traverse  all  corners  of 
the  earth,  and  others  to  prepare  a  larger  caldron  than  had  ever  yet 
been  set  upon  Hecla.  The  affairs  of  Europe  were  at  a  stand  :  its 
balance  was  thrown  aside ;  prime  ministers  and  ambassadors  were 
every  where  in  the  utmost  confusion ;  and,  by  the  way,  they  have 
never  been  able  to  find  the  balance  since  that  time,  and  all  the  fine 
speeches  upon  the  subject,  witli  which  your  newspapers  are  every  now 
and  then  filled,  are  all  mere  hocus-pocus  and  rhodomontade.  How- 
ever, the  caldron  was  soon  set  on,  and  the  air  was  darkened  by  witches 
riding  on  broomsticks,  bringing  a  couple  of  folios  under  each  arm,  and 
across  each  shoulder.  I  remember  the  time  exactly:  it  was  just  as  the 
council  of  Nice  had  broken  up,  so  that  they  got  books  and  papers  there 
dog  cheap ;  but  it  was  a  bad  thing  for  the  poor  English,  as  these  were 
the  worst  materials  that  entered  into  the  caldron.  Besides,  as  the 
Devil  wanted  some  amusement,  and  had  not  seen  an  account  of  the 
transactions  of  this  famous  council,  he  had  all  the  books  brought  from 
it  laid  before  him,  and  split  his  sides  almost  with  laughing,  whilst  he 
was  reading  the  speeches  and  decrees  of  so  many  of  his  old  friends  and 
acquaintance.  All  this  while  the  witches  were  depositing  their  loads 
in  the  great  caldron.  There  were  books  from  the  Dalai  Lama,  and 
from  China :  there  were  books  from  the  Hindoos,  and  tallies  from  the 
Caffres  :  there  were  paintings  from  Mexico,  and  rocks  of  hieroglyphics 
from  Egypt :  the  last  country  supplied  besides  the  swathings  of  two 
thousand  mummies,  and  four-fifths  of  the  famed  library  of  Alexandi-ia. 
Bubble !  bubble  !  toil  and  trouble  !  never  was  a  day  of  more  labour 
and  anxiety  ;  and  if  our  good  master  had  but  flung  in  the  Greek  books 
at  the  proper  time,  they  would  have  made  a  complete  job  of  it.  He 


EARLY   GENIUS.  131 

was  a  little  too  impatient :  as  the  caldron  frothed  up,  he  skimmed  it 
off  with  a  great  ladle,  and  filled  some  thousands  of  our  wind-bags 
with  the  froth,  which  the  English  with  great  joy  carried  back  to  their 
own  country.  These  bags  were  sent  to  every  district :  the  chiefs  first 
took  their  fill,  and  then  the  common  people ;  hence  they  now  speak 
a  language  which  no  foreigner  can  understand,  unless  he  has  learned 
half  a  dozen  other  languages ;  and  the  poor  people,  not  one  in  ten, 
understand  a  third  part  of  what  is  said  to  them.  The  hissing,  how- 
ever, they  have  not  entirely  got  rid  of,  and  every  seven  years,  when 
the  Devil,  according  to  agreement,  pays  them  a  visit,  they  entertain 
him  at  their  common  halls  and  county  meetings  with  their  original 
language. 

The  good  natured  old  hag  told  me  several  other  circumstances, 
relative  to  this  curious  transaction,  which,  as  there  is  an  Englishman 
in  company,  it  will  be  prudent  to  pass  over  in  silence :  but  I  cannot 
help  mentioning  one  thing  which  she  told  me  as  a  very  great  secret. 
You  know,  says  she  to  me,  that  the  English  have  more  religions  among 
them  than  any  other  nation  in  Europe,  and  that  there  is  more  teaching 
and  sermonizing  with  them  than  in  any  other  country.  The  fact  is 
this  ;  it  matters  not  who  gets  up  to  teach  them,  the  hard  words  of  the 
Greek  were  not  sufficiently  boiled,  and  whenever  they  get  into  a 
sentence,  the  poor  people's  brains  are  turned,  and  they  know  no  more 
what  the  preacher  is  talking  about,  than  if  he  harangued  them  in 
Arabic.  Take  my  word  for  it  if  you  please  ;  but  if  not,  when  you  get 
to  England,  desire  the  bettermost  sort  of  people  that  you  are  acquainted 
with  to  read  to  you  an  act  of  parliament,  which  of  course  is  written  in 
the  clearest  and  plainest  stile  in  which  any  thing  can  be  written,  and 
you  will  find  that  not  one  in  ten  will  be  able  to  make  tolerable  sense 
of  it.  The  language  would  have  been  an  excellent  language,  if  it  had 
not  been  for  the  council  of  Nice,  and  the  words  had  been  well  boiled. 

Here  the  company  burst  out  into  a  fit  of  laughter.  The  Englishman 
got  up  and  shook  hands  with  the  Swede :  si  non  e  vero,  said  he,  e  ben 
trovato.  But,  however  I  may  laugh  at  it  here,  I  would  not  advise 
you  to  tell  this  story  on  the  other  side  of  the  water.  So  here's  a 
bumper  to  Old  England  for  ever,  and  God  save  the  king.' 


The  accounts  given  of  extraordinary  children  and  adolescents 
frequently  defy  credence.  I  will  give  two  well-attested  instances. 

The  celebrated  mathematician,  Alexis  Claude  Clairault  (now 
Clairaut)  was  certainly  born  in  May,  1713.  His  treatise  on 
curves  of  double  curvature  (printed  in  1731)  received  the  appro- 
bation of  the  Academy  of  Sciences,  August  23,  1729.  Fontenelle, 
in  his  certificate  of  this,  calls  the  author  sixteen  years  of  age,  and 

K    2 


A  BUDGET   OF  PARADOXES. 

does  not  strive  to  exaggerate  the  wonder,  as  he  might  have  done, 
by  reminding  his  readers  that  this  work,  of  original  and  sustained 
mathematical  investigation,  must  have  been  coming  from  the  pen 
at  the  ages  of  fourteen  and  fifteen.  The  truth  was,  as  attested 
by  De  Molieres,  Clairaut  had  given  public  proofs  of  his  power  at 
twelve  years  old.  His  age  being  thus  publicly  certified,  all  doubt 
is  removed :  say  he  had  been — though  great  wonder  would  still 
have  been  left — twenty-one  instead  of  sixteen,  his  appearance, 
and  the  remembrances  of  his  friends,  schoolfellows,  &c.,  would 
have  made  it  utterly  hopeless  to  knock  off  five  years  of  that  age 
while  he  was  on  view  in  Paris  as  a  young  lion.  De  Molieres,  who 
examined  the  work  officially  for  the  Garde  des  Sceaux,  is  trans- 
ported beyond  the  bounds  of  official  gravity,  and  says  that  it  *  ne 
merite  pas  seulement  d'etre  imprime,  mais  d'etre  admire  comme 
im  prodige  d'imagination,  de  conception,  et  de  capacite.' 

That  Blaise  Pascal  was  born  in  June,  1623,  is  perfectly  well 
established  and  uncontested.  That  he  wrote  his  conic  sections  at 
the  age  of  sixteen  might  be  difficult  to  establish,  though  tolerably 
well  attested,  if  it  were  not  for  one  circumstance,  for  the  book 
was  not  published.  The  celebrated  theorem,  Pascal's  hexagram, 
makes  all  the  rest  come  very  easy.  Now  Curabelle,  in  a  work 
published  in  1644,  sneers  at  Desargues,  whom  he  quotes,  for 
having,  in  1642,  deferred  a  discussion  until  cette  grande  proposi- 
tion nommee  la  Pascale  vei^ra  le  jour.  That  is,  by  the  time 
Pascal  was  nineteen,  the  hexagram  was  circulating  under  a  name 
derived  from  the  author.  The  common  story  about  Pascal, 
given  by  his  sister,  is  an  absurdity  which  no  doubt  has  prejudiced 
many  against  tales  of  early  proficiency.  He  is  made,  when  quite 
a  boy,  to  invent  geometry  in  the  order  of  Euclid's  propositions  : 
as  if  that  order  were  natural  sequence  of  investigation.  The 
hexagram  at  ten  years  old  would  be  a  hundred  times  less  un- 
likely. 

The  instances  named  are  painfully  astonishing :  I  give  one 
which  has  fallen  out  of  sight,  because  it  will  preserve  an  imperfect 
biography.  John  Wilson  is  Wilson  of  that  Ilk,  that  is,  of 
Wilson's  Theorem.-.  It  is  this  :  If  p  be  a  prime  number,  the 
product  of  all  the  numbers  up  to  p  -1,  increased  by  1,  is  divisible 
without  remainder  by  p.  All  mathematicians  know  this  as 
Wilson's  theorem,  but  few  know  who  Wilson  was.  He  was  born 
August  6,  1741,  at  the  Howe  in  Applethwaite,  and  he  was  heir 
to  a  small  estate  at  Troutbeck  in  Westmoreland.  He  was  sent  to 
Peterhouse,  at  Cambridge,  and,  while  an  undergraduate  was 
considered  stronger  in  algebra  than  any  one  in  the  University, 


JOHN  WILSON— WILLIAM  MORGAN— MRS.  FRY.  133 

except  Professor  Waring,  one  of  the  most  powerful  algebraists  of 
the  century.1     He  was  the  senior  wrangler  of  1761,  and  was  then 
for  some  time  a  private  tutor.     When  Paley,  then  in  his  third 
year,  determined  to  make  a  push  for  the  senior  wranglership, 
which  he  got,  Wilson  was  recommended  to  him  as  a  tutor.     Both 
were  ardent  in  their  work,  except  that  sometimes  Paley,  when  he 
came  for  his  lesson,  would  find  gone  a  fishing  written  on  his 
tutor's  outer  door:  which  was  insult  added  to  injury,  for  Paley 
was  very  fond  of  fishing.     Wilson  soon  left  Cambridge,  and  went 
to    the   bar.     He   practised  on  the  northern  circuit  with  great 
success ;  and,  one  day,  while  passing  his  vacation  on  his  little 
property   at   Troutbeck,  he   received  information,  to   his   great 
surprise,  that  Lord  Thurlow,  with  whom  he  had  no  acquaintance, 
had  recommended  him  to  be  a  Judge  of  the  Court  of  Common 
Pleas.     He  died,  Oct.  18,   1793,  with    a  very  high  reputation 
as  a  lawyer  and  a  Judge.     These  facts  are  partly  from  Meadley'a 
'  Life  of  Paley,'  no  doubt   from  Paley  himself,  partly  from  the 
Gentleman's  Magazine,  and  from  an  epitaph  written  by  Bishop 
Watson.     Wilson    did   not  publish  anything :    the   theorem  by 
which  he  has  cut  his  name  in  the  theory  of  numbers  was  com- 
municated to  Waring,  by  whom  it  was  published.     He  married, 
in    1788,  a  daughter  of  Serjeant  Adair,  and  left  issue.     Had  a 
family,  many  will  say :  but  a  man  and  his  wife  are  a  family,  even 
without  children.     An  actuary  may  be  allowed  to  be  accurate  in 
this  matter,  of  which  I  was  reminded  by  what  an  actuary  wrote 
of  another  actuary.     William  Morgan,  in  the  life  of  his  uncle 
Dr.  Richard  Price,  says  that  the  Doctor  and  his  wife  were  '  never 
blessed  with  an  addition  to  their  family.'     I  never  met  "with  such 
accuracy  elsewhere.     Of  William  Morgan  I  add  that  my  surname 
and  pursuits  have  sometimes,  to  my  credit  be  it  said,  made  a 
confusion   between   him   and   me.      Dates   are   nothing   to  the 
xuistaken  ;    the  last  three  years  of  Morgan's  life  were  the  first 
three  years  of  my  actuary-life  (1830-33).     The  mistake  was  to 
my  advantage  as  well  as  to  my  credit.     I  owe  to  it  the  acquaint- 
ance of  one  of  the  noblest  of  the  human  race,  I  mean  Elizabeth 
Fry,  who  came  to  me  for  advice  about  a  philanthropic  design, 
which  involved  life  questions,  under  a  general  impression  that 
some  Morgan  had  attended  to  such  things.2 

1  He  wrote,  in  1760,  a  tract  in  defence  of  Waring,  a  point  of  whose  algebra  had 
been  assailed  by  a  Dr.  Powell.     Waring  wrote  another  tract  of  the  same  date. 

2  Mrs.  Fry  certainly  believed  that  the  writer  was  the  old  actuary  of  the  Equitable, 
when  she  first  consulted  him  upon  the  benevolent  Assurance  project ;  but  we  were 
introduced  to  her  by  our  old  and  dear  friend  Lady  Noel  Byron,  by  whom  she  had 


134  A  BUDGET  OF  PARADOXES. 


A  treatise  on  the  sublime  science  of  heliography,  satisfactorily 
demonstrating  our  great  orb  of  light,  the  sun,  to  be  absolutely 
no  other  than  a  body  of  ice !  Overturning  all  the  received 
systems  of  the  universe  hitherto  extant ;  proving  the  celebrated 
and  indefatigable  Sir  Isaac  Newton,  in  his  theory  of  the  solar 
system,  to  be  as  far  distant  from  the  truth,  as  any  of  the 
heathen  authors  of  Greece  or  Borne.  By  Charles  Palmer,  Gent. 
London,  1798,  8vo. 

Mr.  Palmer  burned  some  tobacco  with  a  burning  glass,  saw 
that  a  lens  of  ice  would  do  as  well,  and  then  says — 

'  If  we  admit  that  the  sun  could  be  removed,  and  a  terrestrial  body 
of  ice  placed  in  its  stead,  it  would  produce  the  same  effect.  The  sun 
is  a  crystaline  body  receiving  the  radience  of  God,  and  operates  on  this 
earth  in  a  similar  manner  as  the  light  of  the  sun  does  when  applied  to 
a  convex  mirror  or  glass.' 

Nov.  10,  1801.  The  Eev.  Thomas  Cormouls,  minister  of 
Tettenhall,  addressed  a  letter  to  Sir  Wm.  Herschel,  from  which  I 
extract  the  following : — 

Here  it  may  be  asked,  then,  how  came  the  doctrines  of  Newton  to 
solve  all  astronomic  Phenomina,  and  all  problems  concerning  the  same, 
both  a  parte  ante  and  a  parte  post.  It  is  answered  that  he  certainly 
wrought  the  principles  he  made  use  of  into  strickt  analogy  with  the 
real  Phenomina  of  the  heavens,  and  that  the  rules  and  results  arizing 
from  them  agree  with  them  and  resolve  accurately  all  questions  con- 
cerning them.  Though  they  are  not  fact  and  true,  or  nature,  but 
analogous  to  it,  in  the  manner  of  the  artificial  numbers  of  logarithms, 
sines,  &c.  A  very  important  question  arises  here,  Did  Newton  mean 
to  impose  upon  the  world  ?  By  no  means :  he  received  and  used  the 
doctrines  reddy  formed ;  he  did  a  little  extend  and  contract  his  prin- 
ciples when  wanted,  and  commit  a  few  oversights  of  consequences.  But 
when  he  was  very  much  advanced  in  life,  he  suspected  the  fundamental 
nullity  of  them  :  but  I  have  from  a  certain  anecdote  strong  ground  to 
believe  that  he  knew  it  before  his  decease,  and  intended  to  have  re- 
tracted his  error.  But,  however,  somebody  did  deceive,  if  not  wilfully, 
neglently  at  least.  That  was  a  man  to  whom  the  world  has  great 
obligations  too.  It  was  no  less  a  philosopher  than  Galileo. 

That  Newton  wanted  to  retract  before  his  death,  is  a  notion 
not   uncommon  among  paradoxers.      Nevertheless,   there  is  no 

been  long  known  and  venerated,  and  who  referred  her  to  Mr.  De  Morgan  for  advice. 
An  unusual  degree  of  confidence  in,  and  appreciation  of  each  other,  arose  on  their 
first  meeting  between  the  two,  who  had  so  much  that  was  externally  different,  and  so 
much  that  was  essentially  alike,  in  their  natures. — (Ed.) 


BISHOP  WILKINS'S   WORKS,  135 

retraction  in  the  third  edition  of  the  '  Principia,'  published  when 
Newton  was  eighty-four  years  old !  The  moral  of  the  above  is, 
that  a  gentleman  who  prefers  instructing  William  Herschel  to 
learning  how  to  spell,  may  find  a  proper  niche  in  a  proper  place, 
for  warning  to  others.  It  seems  that  gravitation  is  not  truth, 
but  only  the  logarithm  of  it. 

The  mathematical  and  philosophical  works  of  the  Right  Rev. 
John  Wilkins  ...  In  two  volumes.     London,  1802,  8vo. 

This  work,  or  at  least  part  of  the  edition — all  for  aught  I  know 
— is  printed  on  wood ;  that  is,  on  paper  made  from  wood-pulp. 
It  has  a  rough  surface,  and  when  held  before  a  candle  is  of  very 
unequal  transparency.  There  is  in  it  a  reprint  of  the  works  on 
the  earth  and  moon.  The  discourse  on  the  possibility  of  going 
to  the  moon,  in  this  and  the  edition  of  1 640,  is  incorporated : 
but  from  the  account  in  the  life  prefixed,  and  a  mention  by 
D'Israeli,  I  should  suppose  that  it  had  originally  a  separate  title- 
page,  and  some  circulation  as  a  separate  tract.  Wilkins  treats 
this  subject  half  seriously,  half  jocosely ;  he  has  evidently  not 
quite  made  up  his  mind.  He  is  clear  that  '  arts  are  not  yet  come 
to  their  solstice,'  and  that  posterity  will  bring  hidden  things  to 
light.  As  to  the  difficulty  of  carrying  food,  he  thinks,  scoffing 
Puritan  that  he  is,  the  Papists  may  be  trained  to  fast  the  voyage, 
or  may  find  the  bread  of  their  Eucharist  '  serve  well  enough  for 
their  viaticum.'  He  also  puts  the  case  that  the  story  of  Do- 
mingo Gonsales  may  be  realized,  namely,  that  wild  geese  find 
their  way  to  the  moon.  It  will  be  remembered — to  use  the 
usual  substitute  for,  It  has  been  forgotten — that  the  posthumous 
work  of  Bishop  Francis  Godwin  of  Llandaff  was  published  in 
1638,  the  very  year  of  Wilkins's  first  edition,  in  time  for  him  to 
mention  it  at  the  end.  Godwin  makes  Domingo  Gronsales  get  to 
the  moon  in  a  chariot  drawn  by  wild  geese,  and,  as  old  books 
would  say,  discourses  fully  on  that  head.  It  is  not  a  little 
amusing  that  Wilkins  should  have  been  seriously  accused  of 
plagiarizing  Godwin,  Wilkins  writing  in  earnest,  or  nearly  so, 
and  Godwin  writing  fiction.  It  may  serve  to  show  philosophers 
how  very  near  pure  speculation  comes  to  fable.  From  the 
sublime  to  the  ridiculous  there  is  but  a  step :  which  is  the  sub- 
lime, and  which  the  ridiculous,  every  one  must  settle  for  himself. 
With  me,  good  fiction  is  the  sublime,  and  bad  speculation  the 
ridiculous.  The  number  of  bishops  in  my  list  is  small.  I 
might,  had  I  possessed  the  book,  have  opened  the  list  of  quad- 
rators  with  an  Archbishop  of  Canterbury,  or  at  least  with  a 


136  A  BUDGET   OF  PARADOXES. 

divine  who  was  not  wholly  not  archbishop.  Thomas  Bradwardine 
(Bragvardinus,  Bragadinus)  was  elected  in  1348  ;  the  Pope  put 
in  another,  who  died  unconsecrated  ;  and  Bradwardine  was  again 
elected  in  1 349,  and  lived  five  weeks  longer,  dying,  I  suppose, 
unconfirmed  and  unconsecrated.  Leland  says  he  held  the  see  a 
year,  unus  tantum  annulus,  which  seems  to  be  a  confusion : 
the  whole  business,  from  the  first  election,  took  about  a  year. 
He  squared  the  circle,  and  his  performance  was  printed  at  Paris 
in  1494.  I  have  never  seen  it,  nor  any  work  of  the  author, 
except  a  tract  on  proportion. 

As  Bradwardine's  works  are  very  scarce  indeed,  I  give  two  titles 
from  one  of  the  Libri  catalogues. 

'  ARITHMETIC.  BRAUARDINI  (Thomas)  Ai-ithmetica  speculativa  revisa 
et  correcta  a  Petro  Sanchez  Ciruelo  Aragonesi,  black  letter, 
elegant  woodcut  title-page,  YERY  RARE,  folio.  Parisiis,  per  Thomam 
Anguelast  {pro  Olivier  Senant),  s.a.  circa  1510. 

'  This  book,  by  Thomas  Bradwardine,  Archbishop  of  Canterbury, 
must  be  exceedingly  scarce  as  it  has  escaped  the  notice  of  Pro- 
fessor De  Morgan,  who,  in  his  Arithmetical  Books,  speaks  of  a 
treatise  of  the  same  author  on  proportions,  printed  at  Vienna  in 
1515,  but  does  not  mention  the  present  work. 

'Bradwardine  (Archbp.  T.).  Brauardini  (Thomse)  Geometria 
speculativa,  cum  Tractatu  de  Quadratura  Circuli  bene  revisa  a 
Petro  Sanchez  Ciruelo,  SCARCE,  folio.  Parisiis,  J.  Petit,  1511. 

'  In  this  work  we  find  the  polygones  etoiles,  see  Chasles  (Aperpu,, 
pp.  480,  487,  521,  523,  &c.)  on  the  merit  of  the  discoveries  of 
this  English  mathematician,  who  was  Archbishop  of  Canterbury 
in  the  xivth  Century  (tempore  Edward  III.  A.D.  1349) ;  and 
who  applied  geometry  to  theology.  M.  Chasles  says  that  the 
present  work  of  Bradwardine  contains  "  Une  theorie  nouvelle  qui 
doit  faire  honneur  au  xive  Siecle." ' 

The  titles  do  not  make  it  quite  sure  that  Bradwardine  is  the 
quadrator ;  it  may  be  Peter  Sanchez  after  all. 

Nouvelle  theorie  des  paralleles.  Par  Adolphe  Kircher  [so  signed 
at  the  end  of  the  appendix].  Paris,  1803,  8vo. 

An  alleged  emendation  of  Legendre.  The  author  refers  to 
attempts  by  Hoffman,  1801,  by  Hauff,  1799,  and  to  a  work  of 
Karsten,  or  at  least  a  theory  of  Karsten,  contained  in  '  Tentamen 
novse  parallelarum  theorise  notione  situs  fundatae ;  auctore  Gr.  C. 


ROSSI— W.   SPENCE— PANICS.  137 

Scliwal,  Stuttgardae,  1801,  en  8  vohimes.'  Surely  this  is  a  mis- 
print ;  eight  volumes  on  the  theory  of  parallels  ?  If  there  be 
such  a  work,  I  trust  I  and  it  may  never  meet,  though  ever  so 
far  produced. 

Soluzione  .  .  .  della  quadratura  del  Circolo.  By  Gaetano  Rossi. 
London,  1804,  8vo. 

The  three  remarkable  points  of  this  book  are,  that  the  house- 
hold of  the  Printfe  of  Wales  took  ten  copies,  Signora  Grassini 
sixteen,  and  that  the  circumference  is  3|-  diameters.  That  is, 
the  appetite  of  Grassini  for  quadrature  exceeded  that  of  the 
whole  household  (loggia)  of  the  Prince  of  Wales  in  the  ratio  in 
which  the  semi-circumference  exceeds  the  diameter.  And  these 
are  the  first  two  in  the  list  of  subscribers.  Did  the  author  see 
this  theorem  ? 

Britain  independent  of  commerce  ;  or  proofs,  deduced  from  an  in- 
vestigation into  the  true  causes  of  the  wealth  of  nations,  that  our 
riches,  prosperity,  and  power  are  derived  from  sources  inherent 
in  ourselves,  and  would  not  be  affected,  even  though  our 
commerce  were  annihilated.  By  Wm.  Spence.  4th  edition, 
1808,  8vo. 

A  patriotic  paradox,  being  in  alleviation  of  the  Commerce 
panic  which  the  measures  of  Napoleon  I. — who  felt  our  Commerce, 
while  Mr.  Spence  only  saw  it — had  awakened.  In  this  very 
month  (August,  1866),  the  Pres.  Brit.  Assoc.  has  applied  a 
similar  salve  to  the  coal  panic ;  it  is  fit  that  science,  which 
rubbed  the  sore,  should  find  a  plaster.  We  ought  to  have  an 
iron  panic  and  a  timber  panic ;  and  a  solemn  embassy  to  the 
Americans,  to  beg  them  not  to  whittle,  would  be  desirable. 
There  was  a  gold  panic  beginning,  before  the  new  fields  were 
discovered.  For  myself,  I  am  the  unknown  and  unpitied  victim 
of  a  chronic  gutta-percha  panic :  I  never  could  get  on  without 
it;  to  me,  gutta  percha  and  Eowland  Hill  are  the  great  dis- 
coveries of  our  day ;  and  not  unconnected  either,  gutta  percha 
being  to  the  submarine  post  what  Eowland  Hill  is  to  the  super- 
terrene.  I  should  be  sorry  to  lose  cow-choke — I  gave  up  trying 
to  spell  it  many  years  ago — but  if  gutta  percha  go,  I  go  too. 
I  think,  that  perhaps  when,  five  hundred  years  hence,  the  people 
say  to  the  Brit.  Assoc.  (if  it  then  exist)  « Pray,  gentlemen,  is  it 
not  time  for  the  coal  to  be  exhausted  ?  '  they  will  be  answered  out 
of  Moliere  (who  will  certainly  then  exist) :  Cela  etait  autrefois 
ainsi,  mais  nous  avons  change  taut  cela.  A  great  many  people 


138  A   BUDGET   OF   PABADOXES. 

think  that  if  the  coal  be  used  up,  it  will  be  announced  some 
unexpected  morning  by  all  the  yards  being  shut  up  and  written 
notice  outside,  '  Coal  all  gone  1 '  just  like  the  *  Please,  ma'am, 
there  ain't  no  more  sugar,'  with  which  the  maid  servant  damps 
her  mistress  just  at  breakfast- time.  But  these  persons  should 
be  informed  that  there  is  every  reason  to  think  that  there  will 
be  time,  as  the  city  gentleman  said,  to  venienti  the  occurrite 
morbo. 


An  appeal  to  the  republic  of  letters  in  behalf  of  injured  science, 
from  the  opinions  and  proceedings  of  some  modern  authors  of 
elements  of  geometry.  By  George  Douglas.  Edinburgh, 
1810,  8vo. 

Mr.  Douglas  was  the  author  of  a  very  good  set  of  mathematical 
tables,  and  of  other  works.  He  criticizes  Simson,  Playfair,  and 
others, — sometimes,  I  think,  very  justly.  There  is  a  curious 
phrase,  which  occurs  more  than  once.  When  he  wants  to  say 
that  something  or  other  was  done  before  Simson  or  another  was 
born,  he  says  '  before  he  existed,  at  least  as  an  author.'  He 
seems  to  reserve  the  possibility  of  Simson's  pre-existence,  but  at 
the  same  time  to  assume  that  he  never  wrote  anything  in  his 
previous  state.  Tell  me  that  Simson  pre-existed  in  any  other 
way  than  as  editor  of  some  pre-existent  Euclid  ?  Tell  Apella  ! 

1810.  In  this  year  Jean  Wood,  Professor  of  Mathematics  in 
the  University  of  Virginia  (Eichmond),  addressed  a  printed 
circular  to  'Dr.  Her sch el,  Astronomer,  Greenwich  Observatory.' 
No  mistake  was  more  common  than  the  natural  one  of  imagining 
that  the  Private  Astronomer  of  the  king  was  the  Astronomer 
Royal.  The  letter  was  on  the  difference  of  velocities  of  the  two 
sides  of  the  earth,  arising  from  the  composition  of  the  rotation 
and  the  orbital  motion.  The  paradox  is  a  fair  one,  and 
deserving  of  investigation ;  but,  perhaps  it  would  not  be  easy  to 
deduce  from  it  tides,  trade-winds,  aerolithes,  &c.,  as  Mr.  Wood 
thought  he  had  done  in  a  work  from  which  he  gives  an  extract, 
and  which  he  describes  as  published.  The  composition  of  rota- 
tions, &c.,  is  not  for  the  world  at  large :  the  paradox  of  the 
non-rotation  of  the  moon  about  her  axis  is  an  instance.  How 
many  persons  know  that  when  a  wheel  rolls  on  the  ground,  the 
lowest  point  is  moving  upwards,  the  highest  point  forwards,  and 
the  intermediate  points  in  all  degrees  of  betwixt  and  between  ? 
This  is  too  short  an  explanation,  with  some  good  difficulties. 


PARADOX   WITHOUT   STOPPING.  1:J9 


The  Elements  of  Geometry.     In  2  vols.     [By  the  Rev.  J.  Dobson, 
B.D.]    Cambridge,  1815.     4to. 

Of  this  unpunctuating  paradoxer  I  shall  give  an  account  in  his 
own  way :  he  would  not  stop  for  any  one ;  why  should  I  stop  for  him  ? 
It  is  worth  while  to  try  how  unpunctuated  sentences  will  read. 

The  reverend  J  Dobson  BD  late  fellow  of  saint  Johns  college 
Cambridge  was  rector  of  Brandesburton  in  Yorkshire  he  was 
seventh  wrangler  in  1798  and  died  in  1847  he  was  of  that  sort  of 
eccentricity  which  permits  account  of  his  private  life  if  we  may 
not  rather  say  that  in  such  cases  private  life  becomes  public  there 
is  a  tradition  that  he  was  called  Death  Dobson  on  account  of  his 
head  and  aspect  of  countenance  being  not  very  unlike  the 
ordinary  pictures  of  a  human  skull  his  mode  of  life  is  reported 
to  have  been  very  singular  whenever  he  visited  Cambridge  he  was 
never  known  to  go  twice  to  the  same  inn  he  never  would  sleep  at 
the  rectory  with  another  person  in  the  house  some  ancient  char- 
woman used  to  attend  to  the  house  but  never  slept  in  it  he  has 
been  known  in  the  time  of  coach  travelling  to  have  deferred  his 
return  to  Yorkshire  on  account  of  his  disinclination  to  travel 
with  a  lady  in  the  coach  he  continued  his  mathematical  studies 
until  his  death  and  till  his  executors  sold  the  type  all  his  tracts 
to  the  number  of  five  were  kept  in  type  at  the  university  press 
none  of  these  tracts  had  any  stops  except  full  stops  at  the  end  of 
paragraphs  only  neither  had  they  capitals  except  one  at  the 
beginning  of  a  paragraph  so  that  a  full  stop  was  generally 
followed  by  some  white  as  there  is  not  a  single  proper  name  in 
the  whole  of  the  book  I  have  I  am  not  able  to  say  whether  he 
would  have  used  capitals  before  proper  names  I  have  inserted 
them  as  usual  for  which  I  hope  his  spirit  will  forgive  me  if  I  be 
wrong  he  also  published  the  elements  of  geometry  in  two 
volumes  quarto  Cambridge  1815  this  book  had  also  no  stops 
except  when  a  comma  was  wanted  between  letters  as  in  the 
straight  lines  AB,  BC  I  should  also  say  that  though  the  title  is 
unpunctuated  in  the  author's  part  it  seems  the  publishers  would 
not  stand  it  in  their  imprint  this  imprint  is  punctuated  as  usual 
and  Deighton  and  Sons  to  prove  the  completeness  of  their  allegi- 
ance have  managed  that  comma  semicolon  colon  and  period 
shall  all  appear  in  it  why  could  they  not  have  contrived  interro- 
gation and  exclamation  this  is  a  good  precedent  to  establish  the 
separate  right  of  the  publisher  over  the  imprint  it  is  said  that 
only  twenty  of  the  tracts  were  printed  and  very  few  indeed  of  the 
book  on  geometry  it  is  doubtful  whether  any  were  sold  there  is  a 


140  A  BUDGET   OF  PAEADOXES. 

copy  of  the  geometry  in  the  university  library  at  Cambridge  and 
I  have  one  myself  the  matter  of  the  geometry  differs  entirely 
from  Euclid  and  is  so  fearfully  prolix  that  I  am  sure  no  mortal 
except  the  author  ever  read  it  the  man  went  on  without  stops 
and  without  stop  save  for  a  period  at  the  end  of  a  paragraph  this 
is  the  unpunctuated  account  of  the  unpunctuating  geometer 
suum  cuique  tribuito  Mrs  Thrale  would  have  been  amused  at  a 
Dobson  who  managed  to  come  to  a  full  stop  without  either  of  the 
three  warnings. 

I  do  not  find  any  difficulty  in  reading  Dobson's  geometry ;  and 
I  have  read  more  of  it  to  try  reading  without  stops  than  I  should 
have  done  had  it  been  printed  in  the  usual  way.  Those  who  dip 
into  the  middle  of  my  paragraph  may  be  surprised  for  a  moment 
to  see  that  '  on  account  of  his  disinclination  to  travel  with  a 
lady  in  the  coach  he  continued  his  mathematical  studies  until 
his  death  and  [further,  of  course]  until  his  executors  sold  the 
type.'  But  a  person  reading  straight  through  would  hardly  take 
it  so.  I  should  add  that,  in  order  to  give  a  fair  trial,  I  did  not 
compose  as  I  wrote,  but  copied  the  words  of  the  correspondent 
who  gave  me  the  facts,  so  far  as  they  went. 

Philosophic/,  Sacra,  or  the  principles  of  natural  Philosophy.  Ex- 
tracted from  Divine  Revelation.  By  the  Rev.  Samuel  Pike. 
Edited  by  the  Rev.  Samuel  Kittle.  Edinburgh,  1815,  8vo. 

This  is  a  work  of  modified  Hutchinsonianism,  which  I  have 
seen  cited  by  several.  Though  rather  dark  on  the  subject,  it 
seems  not  to  contradict  the  motion  of  the  earth,  or  the  doctrine 
of  gravitation,  Mr.  Kittle  gives  a  list  of  some  Hutchinsonians, 
— as  Bishop  Home  ;  Dr.  Stukeley ;  the  Eev.  W.  Jones,  author  of 
'  Physiological  Disquisitions ; '  Mr.  Spearman,  author  of  '  Letters 
on  the  Septuagint '  and  editor  of  Hutchinson ;  Mr.  Barker, 
author  of  '  Eeflexions  on  Learning ' ;  Dr.  Catcott,  author  of  a 
work  on  the  creation,  &c. ;  Dr.  Robertson,  author  of  a  '  Treatise 
on  the  Hebrew  Language  ; '  Dr.  Hollo  way,  author  of  '  Originals, 
Physical  and  Theological ; '  Dr.  Walter  Hodges,  author  of  a  work 
on  Elohim  ;  Lord  President  Forbes  (ob.  1747). 

The  Eev.  William  Jones,  above  mentioned,  (1726-1800),  the 
friend  and  biographer  of  Bishop  Home,  and  his  stout  defender, 
is  best  known  as  William  Jones  of  Nayland,  who  (1757)  pub- 
lished the  '  Catholic  Doctrine  of  the  Trinity ; '  he  was  also  strong 
for  the  Hutchinsonian  physical  trinity  of  fire,  light,  and  spirit. 
This  well-known  work  was  generally  recommended,  as  the  de- 
fence of  the  orthodox  system,  to  those  who  could  not  go  into  the 


TRINITARIAN   CONTROVERSY. 

learning  of  the  subject.  There  is  now  a  work  more  suited  to 
our  time :  '  The  Rock  of  Ages,'  by  the  Rev.  E.  H.  Bickersteth, 
now  published  by  the  Religious  Tract  Society,  without  date, 
answered  by  the  Rev.  Dr.  Sadler,  in  a  work  (1859)  entitled  Gloria 
Patri,  in  which,  says  Mr.  Bickersteth,  'the  author  has  not 
even  attempted  to  grapple  with  my  main  propositions.'  I  have 
read  largely  on  the  controversy,  and  I  think  I  know  what  this 
means.  Moreover,  when  I  see  the  note  '  There  are  two  other 
passages  to  which  Unitarians  sometimes  refer,  but  the  deduction 
they  draw  from  them  is,  in  each  case,  refuted  by  the  context' — 
I  think  I  see  why  the  two  texts  are  not  named.  Nevertheless, 
the  author  is  a  little  more  disposed  to  yield  to  criticism  than  his 
foregoers ;  he  does  not  insist  on  texts  and  readings  which  the 
greatest  editors  have  rejected.  And  he  writes  with  courtesy,  both 
direct  and  oblique,  towards  his  antagonists  ;  which,  on  his  side 
of  this  subject,  is  like  letting  in  fresh  air.  So  that  I  suspect  the 
two  books  will  together  make  a  tolerably  good  introduction  to 
the  subject  for  those  who  cannot  go  deep.  Mr.  Bickersteth's 
book  is  well  arranged  and  indexed,  which  is  a  point  of  superiority 
to  Jones  of  Nayland.  There  is  a  point  which  I  should  gravely 
recommend  to  writers  on  the  orthodox  side.  The  Unitarians  in 
England  have  frequently  contended  that  the  method  of  proving 
the  divinity  of  Jesus  Christ  from  the  New  Testament  would 
equally  prove  the  divinity  of  Moses.  I  have  not  fallen  in  the 
way  of  any  orthodox  answers  specially  directed  at  the  repeated 
tracts  written  by  Unitarians  in  proof  of  their  assertion.  If  there 
be  any,  they  should  be  more  known  ;  if  there  be  none,  some 
should  be  written.  Which  ever  side  may  be  right,  the  treatment 
of  this  point  would  be  indeed  coming  to  close  quarters.  The 
heterodox  assertion  was  first  supported,  it  is  said,  by  John  Bidle 
or  Biddle  (1615-1662)  of  Magdalen  College,  Oxford,  the  earliest 
of  the  English  Unitarian  writers,  previously  known  by  a  transla- 
tion of  part  of  Virgil  and  part  of  Juvenal.  But  I  cannot  find 
that  he  wrote  on  it.  It  is  the  subject  of  '  aipsa-swu  avaaracris^  or  a 
new  way  of  deciding  old  controversies.  By  Basanistes.  Third 
edition,  enlarged,'  London,  1815,  8vo.  It  is  the  appendix  to  the 
amusing,  'Six  more  letters  to  Grranville  Sharp,  Esq.,  .  .  .  By 
Gregory  Blunt,  Esq.'  London,  8vo.,  1803.  This  much  I  can 
confidently  say,  that  the  study  of  these  tracts  would  prevent 
orthodox  writers  from  some  curious  slips,  which  are  slips  obvious 
to  all  sides  of  opinion.  The  lower  defenders  of  orthodoxy  fre- 
quently vex  the  spirits  of  the  higher  ones. 

Since  writing  the  above  I  have  procured  Dr.  Sadler's  answer. 


142  A  BUDGET  OF  PARADOXES. 

I  thought  I  knew  what  the  challenger  meant  when  he  said  the 
respondent  had  not  grappled  with  his  main  propositions.  I 
should  say  that  he  is  clung  on  to  from  beginning  to  end.  But 
perhaps  Mr.  B.  has  his  own  meaning  of  logical  terms,  such  as 
proposition :  he  certainly  has  his  own  meaning  of  cumulative. 
He  says  his  evidence  is  cumulative ;  not  a  catena,  the  strength  of 
which  is  in  its  weakest  part,  but  distinct  and  independent  lines, 
each  of  which  corroborates  the  other.  This  is  the  very  opposite 
of  cumulative :  it  is  distributive.  When  different  arguments  are 
each  necessary  to  a  conclusion,  the  evidence  is  cumulative ;  when 
any  one  will  do,  even  though  they  strengthen  each  other,  it  is 
distributive.  The  word  cumulative  is  a  synonym  of  the  law  word 
constructive ;  a  whole  which  will  do  made  out  of  parts  which 
separately  will  not.  Lord  Strafford  opens  his  defence  with  the 
use  of  both  words  :  '  They  have  invented  a  kind  of  accumulated 
or  constructive  evidence ;  by  which  many  actions,  either  totally 
innocent  in  themselves,  or  criminal  in  a  much  inferior  degree, 
shall,  when  united,  amount  to  treason.'  The  conclusion  is,  that 
Mr.  B.  is  a  Cambridge  man  ;  the  Oxford  men  do  not  confuse  the 
elementary  terms  of  logic.  0  dear  old  Cambridge !  when  the 
New  Zealander  comes  let  him  find  among  the  relics  of  your  later 
sons  some  proof  of  attention  to  the  elementary  laws  of  thought. 
A  little-go  of  logic,  please ! 

Mr.  B.,  though  apparently  not  a  Hutchinsonian,  has  a  nibble 
at  a  physical  Trinity.  *  If,  as  we  gaze  on  the  sun  shining  in  the 
firmament,  we  see  any  faint  adumbration  of  the  doctrine  of  the 
Trinity  in  the  fontal  orb,  the  light  ever  generated,  and  the  heat 
proceeding  from  the  sun  and  its  beams — threefold  and  yet  one, 
the  sun,  its  light,  and  its  heat, — that  luminous  globe,  and  the 
radiance  ever  flowing  from  it,  are  both  evident  to  the  eye ;  but  the 
vital  warmth  is  felt,  not  seen,  and  is  only  manifested  in  the  life 
it  transfuses  through  creation.  The  proof  of  its  real  existence  is 
self-demonstrating.' 

We  shall  see  how  Kevilo1  illustrates  orthodoxy  by  mathematics. 
It  was  my  duty  to  have  found  one  of  the  many  illustrations  from 
physics ;  but  perhaps  I  should  have  forgotten  it  if  this  instance 
had  not  come  in  my  way.  It  is  very  bad  physics.  The  sun, 
apart  from  its  light,  evident  to  the  eye  !  Heat  more  self-demon- 
strating than  light,  because  felt !  Heat  only  manifested  by  the 
life  it  diffuses !  Light  implied  not  necessary  to  life !  But  the 
theology  is  worse  than  Sabellianism.  To  adumbrate — i.e.  make 

1  The  name  assumed  by  a  "writer  who  professed  to  give  a  mathematical  explanation 
of  the  Trinity,  see  farther  on. — (Ed.) 


TRINITARIAN   CONTROVERSY— SIR   RICHARD   PHILLIPS.      143 

a  picture  of — the  orthodox  doctrine,  the  sun  must  be  heavenly 
body,  the  light  heavenly  body,  the  heat  heavenly  body :  and 
yet,  not  three  heavenly  bodies,  but  one  heavenly  body.  The 
truth  is,  that  this  illustration  and  many  others  most  strik- 
ingly illustrate  the  Trinity  of  fundamental  doctrine  held  by  the 
Unitarians,  in  all  its  differences  from  the  Trinity  of  persons  held 
by  the  Orthodox.  Be  right  which  may,  the  right  or  wrong  of 
the  Unitarians  shines  out  in  the  comparison.  Dr.  Sadler  confirms 
me — by  which  I  mean  that  I  wrote  the  above  before  I  saw  what 
he  says — in  the  following  words  :  '  The  sun  is  one  object  with  two 
properties,  and  these  properties  have  a  parallel  not  in  the  second 
and  third  persons  of  the  Trinity,  but  in  the  attributes  of  Deity.' 

The  letting  light  alone,  as  self-evident,  and  making  heat  self- 
demonstrating,  because  felt — i.e.  perceptible  now  and  then — has 
the  character  of  the  Irishman's  astronomy  : — 

Long  life  to  the  moon,  for  a  dear  noble  cratur, 
Which  serves  us  for  lamplight  all  night  in  the  dark, 
While  the  sun  only  shines  in  the  day,  which,  by  natur, 
Wants  no  light  at  all,  as  ye  all  may  remark. 

Sir  Richard  Phillips  (born  1768)  was  conspicuous  in  1793, 
when  he  was  sentenced  to  a  year's  imprisonment  for  selling 
Paine's  '  Eights  of  Man ; '  and  again  when,  in  1 807,  he  was 
knighted  as  Sheriff  of  London.  As  a  bookseller,  he  was  able  to 
enforce  his  astronomical  opinions  in  more  ways  than  others. 
For  instance,  in  James  Mitchell's  'Dictionary  of  the  Mathe- 
matical and  Physical  Sciences,'  1823,  12mo.,  which,  though  he 
was  not  technically  a  publisher,  was  printed  for  him — a  book  I 
should  recommend  to  the  collector  of  works  of  reference — there 
is  a  temperate  description  of  his  doctrines,  which  one  may  almost 
swear  was  one  of  his  conditions  previous  to  undertaking  the  work. 
Phillips  himself  was  not  only  an  anti-Newtonian,  but  carried  to  a 
fearful  excess  the  notion  that  statesmen  and  Newtonians  were 
in  league  to  deceive  the  world.  He  saw  this  plot  in  Mrs.  Airy's 
pension,  and  in  Mrs.  Somerville's.  In  1836,  he  did  me  the 
honour  to  attempt  my  conversion.  In  his  first  letter  he  says  : — 

Sir  Richard  Phillips  has  an  inveterate  abhorrence  of  all  the  pre- 
tended wisdom  of  philosophy  derived  from  the  monks  and  doctors  of 
the  middle  ages,  and  not  less  of  those  of  higher  name  who  merely 
sought  to  make  the  monkish  philosophy  more  plausible,  or  so  to  dis- 
guise it  as  to  mystify  the  mob  of  small  thinkers. 

So  little  did  his  writings  show  any  knowledge  of  antiquity, 
that  I  strongly  suspect,  if  required  to  name  one  of  the  monkish 


144  A  BUDGET  OF  PAKADOXES. 

doctors,  he  would  have  answered — Aristotle.  These  schoolmen, 
and  the  '  philosophical  trinity  of  gravitating  force,  projectile 
force,  and  void  space,'  were  the  bogies  of  his  life. 

I  think  he  began  to  publish  speculations  in  the  Monthly 
Magazine  (of  which  he  was  editor)  in  July  1817  :  these  he 
republished  separately  in  1818.  In  the  Preface,  perhaps  judging 
the  feelings  of  others  by  his  own,  he  says  that  he  '  fully  expects 
to  be  vilified,  reviled,  and  anathematized,  for  many  years  to 
come.'  Poor  man!  he  was  let  alone.  He  appeals  with  con^ 
fidence  to  the  '  impartial  decision  of  posterity ; '  but  posterity 
does  not  appoint  a  hearing  for  one  per  cent,  of  the  appeals  which 
are  made ;  and  it  is  much  to  be  feared  that  an  article  in  such  a 
work  of  reference  as  this  will  furnish  nearly  all  her  materials  fifty 
years  hence.  The  following,  addressed  to  M.  Arago,  in  1835, 
will  give  posterity  as  good  a  notion  as  she  will  probably  need : — 

Even  the  present  year  has  afforded  EVER-MEMORABLE  examples, 
paralleled  only  by  that  of  the  Romish  Conclave  which  persecuted 
Galileo.  Policy  has  adopted  that  maxim  of  Machiavel  which  teaches 
that  it  is  more  prudent  to  reward  partisans  than  to  persecute  opponents. 
Hence,  a  bigotted  party  had  influence  enough  with  the  late  short-lived 
administration  [I  think  lie  is  wrong  as  to  the  administration]  of 
Wellington,  Peel,  &c.,  to  confer  munificent  royal  pensions  on  three 
writers  whose  sole  distinction  was  their  advocacy  of  the  Newtonian 
philosophy.  A  Cambridge  professor  last  year  published  an  elaborate 
volume  in  illustration  of  Gravitation,  and  on  him  has  been  conferred  a 
pension  of  300Z.  per  annum.  A  lady  has  written  a  light  popular  view 
of  the  Newtonian  Dogmas,  and  she  has  been  complimented  by  a  pension 
of  200Z.  per  annum.  And  another  writer,  who  has  recently  published 
a  volume  to  prove  that  the  only  true  philosophy  is  that  of  Moses,  has 
been  endowed  with  a  pension  of  2007.  per  annum.  Neither  of  them 
were  needy  persons,  and  the  political  and  ecclesiastical  bearing  of  the 
whole  was  indicated  by  another  pension  of  300Z.  bestowed  on  a  political 
•writer,  the  advocate  of  all  abuses  and  prejudices.  Whether  the  con- 
duct of  the  Romish.  Conclave  was  more  base  for  visiting  with  legal 
penalties  the  promulgation  of  the  doctrines  that  the  Earth  turns  on  its 
axis  and  revolves  around  the  Sun ;  or  that  of  the  British  Court,  for  its 
craft  in  conferring  pensions  on  the  opponents  of  the  plain  corollary, 
that  all  the  motions  on  the  Earth  are  '  part  and  parcel '  of  these  great 
motions,  and  those  again  and  all  like  them  consecutive  displays  of 
still  greater  motions  in  equality  of  action  and  reaction,  is  A  QUESTION 
which  must  be  reserved  for  the  casuists  of  other  generations.  .  .  I 
cannot  expect  that  on  a  sudden  you  and  your  friends  will  come  to  my 
conclusion,  that  the  present  philosophy  of  the  Schools  and  Univer- 
sities of  Europe,  based  on  faith  in  witchcraft,  magic,  &c.,  is  a  system 
of  execrable  nonsense,  by  which  quacks  live  on  the  faith  of  fools  ;  but  I 
desire  a  free  and  fair  examination  of  my  Aphorisms,  and  if  a  few  are 


PHILLIPS— WOOD- SATIRICAL  PARADOX.  145 

admitted  to  be  true,  merely  as  courteous  concessions  to  arithmetic,  my 
purpose  will  be  effected,  for  men  will  thus  be  led  to  think ;  and  if  they 
think,  then  the  fabric  of  false  assumptions,  and  degrading  superstitions 
will  soon  tumble  in  ruins. 

This  for  posterity.  For  the  present  time  I  ground  the  fame  of 
Sir  Pt.  Phillips  on  his  having  squared  the  circle  without  knowing 
it,  or  intending  to  do  it.  '  •  In  the  Protest  presently  noted  he 
discovered  that  '  the  force  taken  as  1  is  equal  to  the  sum  of  all 
its  fractions  ....  thus  1  =  i  +  §-  +  TV  +  aV?  &c-j  carried  to  in- 
finity.' This  the  mathematician  instantly  sees  is  equivalent  to 
the  theorem  that  the  circumference  of  any  circle  is  double  of  the 
diagonal  of  the  cube  on  its  diameter. 

I  have  examined  the  following  works  of  Sir  E.  Phillips,  and 
heard  of  many  others  : — 

Essays  on  the  proximate  mechanical  causes  of  the  general  phe- 
nomena of  the  Universe,  1818,  12mo. 

Protest  against  the  prevailing  principles  of  natural  philosophy, 
with  the  development  of  a  common  sense  system  (no  date, 
8vo.  pp.  16). 

Four  dialogues  between  an  Oxford  Tutor  and  a  disciple  of  the 
common-sense  philosophy,  relative  to  the  proximate  causes  of 
material  phenomena.  8vo.  1824. 

A  century  of  original  aphorisms  on  the  proximate  causes  of  the 
phenomena  of  nature,  1835,  12mo. 

Sir  Richard  Phillips  had  four  valuable  qualities ;  honesty, 
zeal,  ability,  and  courage.  He  applied  them  all  to  teaching 
matters  about  which  he  knew  nothing ;  and  gained  himself  an 
uncomfortable  life  and  a  ridiculous  memory. 

Astronomy  made  plain ;  or  only  way  the  true  perpendicular  dis- 
tance of  the  Sun,  Moon,  or  Stars,  from  this  earth,  can  be 
obtained.  By  Wm.  Wood.  Chatham,  1819,  12mo. 

If  this  theory  be  true,  it  will  follow,  of  course,  that  this  earth  is  the 
only  one  God  made,  and  that  it  does  not  whirl  round  the  sun,  but  vice 
versa,  the  sun  round  it. 

Historic  doubts  relative  to  Napoleon  Buonaparte.     London,  ]  819, 

8vo. 

This  tract  has  since  been  acknowledged  by  Archbishop 
"\Vhately  and  reprinted.  It  is  certainly  a  paradox :  but  differs 
from  most  of  those  in  my  list  as  being  a  joke,  and  a  satire  upon 
the  reasoning  of  those  who  cannot  receive  narrative,  no  matter 

L 


146  A   BUDGET   OF  PAKADOXES. 

what  the  evidence,  which  is  to  them  utterly  improbable  a  priori. 
But  had  it  been  serious  earnest,  it  would  not  have  been  so  absurd 
as  many  of  those  which  I  have  brought  forward.  The  next  on 
the  list  is  not  a  joke. 

The  idea  of  the  satire  is  not  new.  Dr.  King,  in  the  dispute 
on  the  genuineness  of  Phalaris,  proved  with  humour  that  Bentley 
did  not  write  his  own  dissertation.  An  attempt  has  lately  been 
made,  for  the  honour  of  Moses,  to  prove,  without  humour,  that 
Bishop  Colenso  did  not  write  his  own  book.  This  is  intolerable  : 
anybody  who  tries  to  use  such  a  weapon  without  banter,  plenty 
and  good,  and  of  form  suited  to  the  subject,  should  get  the 
drubbing  which  the  poor  man  got  in  the  Oriental  tale  for  striking 
the  dervishes  with  the  wrong  hand. 

The  excellent  and  distinguished  author  of  this  tract  has  ceased 
to  live.  I  call  him  the  Paley  of  our  day :  with  more  learning, 
and  more  purpose  than  his  predecessor ;  but  perhaps  they  might 
have  changed  places  if  they  had  changed  centuries.  The  clever 
satire  above  named  is  not  the  only  work  which  he  published 
without  his  name.  The  following  was  attributed  to  him,  I 
believe  rightly :  '  Considerations  on  the  Law  of  Libel,  as  relating 
to  Publications  on  the  subject  of  Eeligion,  by  John  Search.' 
London,  1833,  8vo.  This  tract  excited  little  attention:  for  those 
who  should  have  answered,  could  not.  Moreover,  it  wanted  a 
prosecution  to  call  attention  to  it :  the  fear  of  calling  such  atten- 
tion may  have  prevented  prosecutions.  Those  who  have  read  it 
will  have  seen  why. 

The  theological  review  elsewhere  mentioned  attributes  the 
pamphlet  of  John  Search  on  blasphemous  libel  to  Lord  Brougham. 
This  is  quite  absurd  :  the  writer  states  points  of  law  on  credence 
where  the  judge  must  have  spoken  with  authority.  Besides  which, 
a  hundred  points  of  style  are  decisive  between  the  two.  I  think 
any  one  who  knows  Whately's  writings  will  soon  arrive  at  my 
conclusion.  Lord  Brougham  himself  informs  me  that  he  has  no 
knowledge  whatever  of  the  pamphlet. 

It  is  stated  in  Notes  and  Queries  (3  S.  xi.  511)  that  Search 
was  answered  by  the  Bishop  of  P'erns  as  S.N.,  with  a  rejoinder  by 
Blanco  White.  These  circumstances  increase  the  probability  that 
Whately  was  written  against  and  for. 

Voltaire  Chretien ;  preuves  tirees  de  ses  ouvrages.     Paris,  1820, 
12mo. 

If  Voltaire  have  not  succeeded  in  proving  himself  a  strong 
theist  and  a  strong  anti-revelationist,  who  is  to  succeed  in  proving 


THE  WORD  CHRISTIAN.  147 

himself  one  thing  or  the  other  in  any  matter  whatsoever  ?  By 
occasional  confusion  between  theism  and  Christianity ;  by  taking 
advantage  of  the  formal  phrases  of  adhesion  to  the  Eoman 
Church,  which  very  often  occur,  and  are  often  the  happiest  bits 
of  irony  in  an  ironical  production  ;  by  citations  of  his  morality, 
which  is  decidedly  Christian,  though  often  attributed  to  Brah- 
mins ;  and  so  on — the  author  makes  a  fair  case  for  his  paradox, 
in  the  eyes  of  those  who  know  no  more  than  he  tells  them.  If 
he  had  said  that  Voltaire  was  a  better  Christian  than  himself 
knew  of,  towards  all  mankind  except  men  of  letters,  I  for  one 
should  have  agreed  with  him. 

Christian  !  the  word  has  degenerated  into  a  synonym  of  man, 
in  what  are  called  Christian  countries.  So  we  have  the  porrot 
who  '  swore  for  all  the  world  like  a  Christian,'  and  the  two  dogs 
who  '  hated  each  other  just  like  Christians.'  When  the  Irish 
duellist  of  the  last  century,  whose  name  may  be  spared  in 
consideration  of  its  historic  fame  and  the  worthy  people  who 
bear  it,  was  (June  12,  1786)  about  to  take  the  consequence  of 
his  last  brutal  murder,  the  rope  broke,  and  the  criminal  got  up, 

and  exclaimed,  l  By Mr.  Sheriff,  you  ought  to  be  ashamed 

of  yourself !  this  rope  is  not  strong  enough  to  hang  a  dog,  far 
less  a  Christian  ! '  But  such  things  as  this  are  far  from  the  worst 
depravations.  As  to  a  word  so  defiled  by  usage,  it  is  well  to 
know  that  there  is  a  way  of  escape  from  it,  without  renouncing 
the  New  Testament.  I  suppose  any  one  may  assume  for  himself 
what  I  have  sometimes  heard  contended  for,  that  no  New  Testa- 
ment word  is  to  be  used  in  religion  in  any  sense  except  that  of 
the  New  Testament.  This  granted,  the  question  is  settled. 
The  word  Christian,  which  occurs  three  times,  is  never  recog- 
nised as  anything  but  a  term  of  contempt  from  those  without 
the  pale  to  those  within.  Thus,  Herod  Agrippa,  who  was  deep  in 
Jewish  literature,  and  a  correspondent  of  Josephus,  says  to  Paul, 
(Acts  xxvi.  28)  '  Almost  thou  persuadest  me  to  be  (what  I  and 
other  followers  of  the  state  religion  depise  under  the  name) 
a  Christian.'  Again,- ( Acts  xi.  26)  'The  disciples  (as  they  called 
themselves)  were  called  (by  the  surrounding  heathens)  Christians 
first  in  Antioch.'  Thirdly,  (1  Peter  iv.  16)  'Let  none  of  you 
suffer  as  a  murderer.  .  .  .  But  if  as  a  Christian  (as  the  heathen 
call  it  by  whom  the  suffering  comes),  let  him  not  be  ashamed.' 
That  is  to  say,  no  disciple  ever  called  himself  a  Christian,  or 
applied  the  name,  as  from  himself,  to  another  disciple,  from  one 
end  of  the  New  Testament  to  the  other ;  and  no  disciple  need 

L    2 


148  A  BUDGET  OF  PARADOXES. 

apply  that  name  to  himself  in  our  day,  if  he  dislike  the  associa- 
tions with  which  the  conduct  of  Christians  has  clothed  it. 

Address  of  M.  Hoene  Wronski  to  the  British  Board  of  Longitude, 

upon  the  actual  state  of  the  mathematics,  their  reform,  and 

upon  the  new  celestial  mechanics,  giving  the  definitive  solution 

of  the  problem  of  longitude.     London,  1820,  8vo. 

M.  Wronski  was  the  author  of  seven  quartos  on  mathematics, 

showing  very  great  power  of  generalization.     He  was  also  deep  in 

the   transcendental   philosophy,   and   had   the   Absolute   at   his 

fingers'  ends.      All  this  knowledge  was   rendered  useless  by  a 

persuasion  that  he  had  greatly  advanced  beyond  the  whole  world, 

with  many  hints  that  the  Absolute  would  not  be  forthcoming, 

unless   prepaid.     He   was   a  man  of  the   widest  extremes.     At 

one  time  he  desired  people  to  see  all  possible  mathematics  in 

Faj= A0O0  +  A1fl1  +  A2O2  +  A3H3  +  &c, 

which  he  did  not  explain,  though  there  is  meaning  to  it  in  the 
quartos.  At  another  time  he  was  proposing  the  general  solution 
of  the  fifth  degree  by  help  of  625  independent  equations  of  one 
form  and  125  of  another.  The  first  separate  memoir  from  any 
Transactions  that  t  ever  possessed  was  given  to  me  when  at 
Cambridge;  the  refutation  (1819)  of  this  asserted  solution, 
presented  to  the  Academy  of  Lisbon  by  Evangelista  Torriano. 
I  cannot  say  I  read  it.  The  tract  above  is  an  attack  on  modern 
mathematicians  in  general,  and  on  the  Board  of  Longitude,  and 
Dr.  Young. 

1820.  In  this  year  died  Dr.  Isaac  Milner,  President  of  Queens' 
College,  Cambridge,  one  of  the  class  of  rational  paradoxers. 
Under  this  name  I  include  all  who,  in  private  life,  and  in  matters 
which  concern  themselves,  take  their  own  course,  and  suit  their 
own  notions,  no  matter  what  other  people  may  think  of  them. 
These  men  will  put  things  to  uses  they  were  never  intended  for, 
to  the  great  distress  and  disgust  of  their  gregarious  friends.  I 
am  one  of  the  class,  and  I  could  write  a  little  book  of  cases  in 
which  I  have  incurred  absolute  reproach  for  not  '  doing  as  other 
people  do.'  I  will  name  two  of  my  atrocities  :  I  took  one  of 
those  butter-dishes  which  have  for  a  top  a  dome  with  holes  in 
it,  which  is  turned  inward,  out  of  reach  of  accident,  when  not  in 
use.  Turning  the  dome  inwards,  I  filled  the  dish  with  water, 
and  put  a  sponge  in  the  dome :  the  holes  let  it  fill  with  water, 
and  I  had  a  penwiper,  always  moist,  and  worth  its  price  five 
times  over.  '  Why !  what  do  you  mean  ?  It  was  made  to  hold 


MILNER'S   LAMP.  149 

butter.  You  are  always  at  some  queer  thing  or  other ! '  I 
bought  a  leaden  comb,  intended  to  dye  the  hair,  it  being  sup- 
posed that  the  application  of  lead  will  have  this  effect.  I  did 
not  try :  but  I  divided  the  comb  into  two,  separating  the  part 
of  closed  prongs  from  the  other ;  and  thus  I  had  two  ruling 
machines.  The  lead  marks  paper,  and  by  drawing  the  end  of 
one  of  the  machines  along  a  ruler,  I  could  rule  twenty  lines  at 
a  time,  quite  fit  to  write  on.  I  thought  I  should  have  killed  a 
friend  to  whom  I  explained  it :  he  could  not  for  the  life  of  him 
understand  how  leaden  lines  on  paper  would  dye  the  hair. 

But  Dr.  Milner  went  beyond  me.  He  wanted  a  seat  suited  to 
his  shape,  and  he  defied  opinion  to  a  fearful  point.  He  spread  a 
thick  block  of  putty  over  a  wooden  chair  and  sat  in  it  until  it 
had  taken  a  ceroplast  copy  of  the  proper  seat.  This  he  gave  to 
a  carpenter  to  be  imitated  in  wood.  One  of  the  few  now  living 
who  knew  him — my  friend,  General  Perronet  Thompson — 
answers  for  the  wood,  which  was  shown  him  by  Milner  himself  ; 
but  he  does  not  vouch  for  the  material  being  putty,  which  was 
in  the  story  told  me  at  Cambridge ;  William  Frend  also  re- 
membered it.  Perhaps  the  Doctor  took  off  his  great  seal  in 
green  wax,  like  the  Crown ;  but  some  soft  material  he  certainly 
adopted ;  and  very  comfortable  he  found  the  wooden  copy. 

The  same  gentleman  vouches  for  Milner's  lamp :  but  this  had 
visible  science  in  it ;  the  vulgar  see 
no  science  in  the  construction  of  the 
chair.  A  hollow  semi-cylinder,  but 
not  with  a  circular  curve,  revolved  on 
pivots.  The  curve  was  calculated  on 
the  law  that,  whatever  quantity  of  oil 
might  be  in  the  lamp,  the  position  of 
equilibrium  just  brought  the  oil  up  to 
the  edge  of  the  cylinder,  at  which  a 
bit  of  wick  was  placed.  As  the  wick 
exhausted  the  oil,  the  cylinder  slowly 
revolved  about  the  pivots  so  as  to 
keep  the  oil  always  touching  the  wick. 

Great  discoveries  are  always  laughed  at :  but  it  is  very  often 
not  the  laugh  of  incredulity  ;  it  is  a  mode  of  distorting  the  sense 
of  inferiority  into  a  sense  of  superiority,  or  a  mimicry  of  supe- 
riority interposed  between  the  laugher  and  his  feeling  of  in- 
feriority. Two  persons  in  conversation  agreed  that  it  was  often 


150  A  BUDGKET  OF  PARADOXES. 

a  nuisance  not  to  be  able  to  lay  hands  on  a  bit  of  paper  to  mark 
the  place  in  a  book,  every  bit  of  paper  on  the  table  was  sure  to 
contain  something  not  to  be  spared.  I  very  quietly  said  that  I 
always  had  a  stock  of  bookmarkers  ready  cut,  with  a  proper  place 
for  them  :  my  readers  owe  many  of  my  anecdotes  to  this  absurd 
practice.  My  two  colloquials  burst  into  a  fit  of  laughter  ;  about 
what  ?  Incredulity  was  out  of  the  question  ;  and  there  could  be 
nothing  foolish  in  my  taking  measures  to  avoid  what  they  knew 
was  an  inconvenience.  I  was  in  this  matter  obviously  their 
superior,  and  so  they  laughed  at  me.  Much  more  candid  was 
the  Eoyal  Duke  of  the  last  century,  who  was  noted  for  slow  ideas. 
'  The  rain  comes  into  my  mouth,'  said  he,  while  riding.  '  Had 
not  your  Royal  Highness  better  shut  your  mouth  ?  '  said  the 
equerry.  The  Prince  did  so,  and  ought,  by  rule,  to  have  laughed 
heartily  at  his  adviser  ;  instead  of  this,  he  said  quietly,  '  It 
doesn't  come  in  now.' 

De  Attentionis  mensura  causisque  primariis.     By  J.  F.  Herbart. 
Koenigsberg,  1822,  4to. 

This  celebrated  philosopher  maintained  that  mathematics 
ought  to  be  applied  to  psychology,  in  a  separate  tract,  published 
also  in  1822  :  the  one  above  seems,  therefore,  to  be  his  challenge 
on  the  subject.  It  is  on  attention,  and  I  think  it  will  hardly 
support  Herbart's  thesis.  As  a  specimen  of  his  formula,  let  t  be 
the  time  elapsed  since  the  consideration  began,  /3  the  whole 
perceptive  intensity  of  the  individual,  (f>  the  whole  of  his  mental 
force,  and  z  the  force  given  to  a  notion  by  attention  during  the 
time  t.  Then, 


Now  for  a  test.  There  is  a  jactura,  v,  the  meaning  of  which  I 
do  not  comprehend.  If  there  be  anything  in  it,  my  mathe- 
matical readers  ought  to  interpret  it  from  the  formula 


1-/3 

and  to  this  task  I  leave  them,  wishing  them  better  luck  than 
mine.  The  time  may  come  when  other  manifestations  of  mind, 
besides  belief,  shall  be  submitted  to  calculation  :  at  that  time, 
should  it  arrive,  a  final  decision  may  be  passed  upon  Herbart. 


THE   WHIZGIG— MYTHOLOGICAL  ASTRONOMY.  151 


The  theory  of  the  Whizgtg  considered  ;  in  as  much  as  it  mechani- 
cally exemplifies  the  three  working  properties  of  nature  ;  which 
are  now  set  forth  under  the  guise  of  this  toy,  for  children  of  all 
ages.  London,  1822,  12mo.  (pp.  24,  B.  McMillan,  Bow  Street, 
Covent  Garden.) 

The  toy  called  the  whizgig  will  be  remembered  by  many.  The 
writer  is  a  follower  of  Jacob  Behmen,  William  Law,  Richard 
Clarke,  and  Eugenius  Philaleth.es.  Jacob  Behmen  first  an- 
nounced the  three  working  properties  of  nature,  which  Newton 
stole,  as  described  in  the  Gentleman's  Magazine,  July,  1782, 
p.  329.  These  laws  are  illustrated  in  the  whizgig.  There  is  the 
harsh  astringent,  attractive  compression  ;  the  bitter  compunction, 
repulsive  expansion ;  and  the  stinging  anguish,  duplex  motion. 
The  author  hints  that  he  has  written  other  works,  to  which  he 
gives  no  clue.  I  have  heard  that  Behmen  was  pillaged  by  New- 
ton, and  Swedenborg  by  Laplace,  and  Pythagoras  by  Copernicus, 
and  Epicurus  by  Dalton,  &c.  I  do  not  think  this  mention  will 
revive  Behmen ;  but  it  may  the  whizgig,  a  very  pretty  toy,  and 
philosophical  withal,  for  few  of  those  who  used  it  could  ex- 
plain it. 

A  Grammar  of  infinite  forms ;  or  the  mathematical  elements  of 
ancient  philosophy  and  mythology.  By  Wm.  Howison.  Edin- 
burgh, 1823,  8vo. 

A  curious  combination  of  geometry  and  mythology.  Perseus, 
for  instance,  is  treated  under  the  head, '  the  evolution  of  diminish- 
ing hyperbolic  branches.' 

The  Mythological  Astronomy  of  the  Ancients ;  part  the  second  : 
or  the  key  of  Urania,  the  wards  of  which  will  unlock  all  the 
mysteries  of  antiquity.  Norwich,  1823,  12mo. 

A  Companion  to  the.  Mythological  Astronomy,  &c.,  containing 
remai'ks  on  recent  publications.  .  .  Norwich,  1824,  12mo. 

A  new  Theory  of  the  Earth  and  of  planetary  motion ;  in  which  it 
is  demonstrated  that  the  Sun  is  vicegerent  of  his  own  system. 
Norwich,  1825,  12mo. 

The  analyzation  of  the  writings  of  the  Jews,  so  far  as  they  are 
found  to  have  any  connection  with  the  sublime  science  of 
astronomy.  [This  is  pp.  97-180  of  some  other  work,  being  all 
I  have  seen.] 

These  works  are  all  by  Sampson  Arnold  Mackey,  for  whom  see 
Notes  and  Queries,  1st  S.  viii.  468,  565,  ix.  89,  179.  Had  it 


J52  A   BUDGET   OF  PARADOXES. 

not  been  for  actual  quotations  given  by  one  correspondent  only 
(1st  S.  viii.  565),  that  journal  would  have  handed  him  down  as 
a  man  of  some  real  learning.  An  extraordinary  man  he  certainly 
was :  it  is  not  one  illiterate  shoemaker  in  a  thousand  who  could  work 
upon  such  a  singular  mass  of  Sanscrit  and  Greek  words,  without 
showing  evidence  of  being  able  to  read  a  line  in  any  language 
but  his  own,  or  to  spell  that  correctly.  He  was  an  uneducated 
Godfrey  Higgins.  A  few  extracts  will  put  this  in  a  strong  light : 
one  for  history  of  science,  one  for  astronomy,  and  one  for  philo- 
logy : — 
&j  v 

'  Sir  Isaac  Newton  was  of  opinion  that  "  the  atmosphere  of  the  earth 
was  the  sensory  of  God  ;  by  which  he  was  enabled  to  see  quite  round 
the  earth  : "  which  proves  that  Sir  Isaac  had  no  idea  that  God  could 
see  through  the  earth. 

Sir  Richard  [Phillips]  has  given  the  most  rational  explanation  of 
the  cause  of  the  earth's  elliptical  orbit  that  I  have  ever  seen  in  print. 
It  is  because  the  earth  presents  its  watery  hemisphere  to  the  sun  at 
one  time  and  that  of  solid  land  the  other ;  but  why  has  he  made  his 
Oxonian  astonished  at  the  coincidence  ?  It  is  what  I  taught  in  my 
attic  twelve  years  before. 

Again,  admitting  that  the  Eloim  were  powerful  and  intelligent  beings 
that  managed  these  things,  we  would  accuse  them  of  being  the  authors 
of  all  the  sufferings  of  Chrisna.  And  as  they  and  the  constellation  of 
Leo  were  below  the  horizon,  and  consequently  cut  off  from  the  end  of 
the  zodiac,  there  were  but  eleven  constellations  of  the  zodiac  to  be 
seen ;  the  three  at  the  end  were  wanted,  but  those  three  would  be 
accused  of  bringing  Chrisna  into  the  troubles  which  at  last  ended  in 
his  death.  All  this  would  be  expressed  in  the  Eastern  language  by 
saying  that  Chrisna  was  persecuted  by  those  Judoth  Isbcariotb  ! !  !  !  ! 
[the  five  notes  of  exclamation  are  the  author's].  But  the  astronomy 
of  those  distant  ages,  when  the  sun  was  at  the  south  pole  in  winter, 
would  leave  five  of  those  Decans  cut  off  from  our  view,  in  the  latitude 
of  twenty-eight  degrees;  hence  Chrisna  died  of  wounds  from  five 
Decans,  but  the  whole  five  may  be  included  in  Judoth  Ishcarioth  !  for 
the  phrase  means  the  men  that  are  wanted  at  the  extreme  parts.  Ish- 
carioth is  a  compound  of  ish,  a  man,  and  carat  wanted  or  taken  away, 
and  oth  the  plural  termination,  more  ancient  than  im. .  . ' 

I  might  show  at  length  how  Michael  is  the  sun,  and  the 
D'-ev-'l,  in  French  Di-ob-al,  also  'L-evi-ath-an — the  evi  being  the 
radical  part  both  of  devil  and  leviathan — is  the  Nile,  which  the 
sun  dried  up  for  Moses  to  pass :  a  battle  celebrated  by  Jude. 
Also  how  Moses,  the  same  name  as  Muses,  is  from  mesha,  drawn 
out  of  the  water,  '  and  hence  we  called  our  land  which  is  saved 
from  the  water  by  the  name  of  marsh.''  But  it  will  be  of  more  use 
to  collect  the  character  of  S.  A.  M.  from  such  correspondents  of 


A  TKANSCENDENTAL  PHILOSOPHER.  153 

Notes  and  Queries  as  have  written  after  superficial  examination. 
Great  astronomical  and  philological  attainments  ;  much  ability 
and  learning;  had  evidently  read  and  studied  deeply;  remark- 
able for  the  originality  of  his  views  upon  the  very  abstruse 
subject  of  mythological  astronomy,  in  which  he  exhibited  great 
sagacity.  Certainly  his  views  were  original ;  but  their  sagacity, 
if  it  be  allowable  to  copy  his  own  mode  of  etymologizing,  is  of  an 
ori-gin-ale  cast,  resembling  that  of  a  person  who  puts  to  his 
mouth  liquors  both  distilled  and  fermented. 

Principles  of  the  Kantesian,  or  transcendental  philosophy.      By 
Thomas  Wirgman.     London,  1824,  8vo. 

Mr.  Wirgman's  mind  was  somewhat  attuned  to  psychology; 
but  he  was  cracky  and  vagarious.  He  had  been  a  fashionable 
jeweller  in  St.  James's  Street,  no  doubt  the  son  or  grandson  of 
Wirgman  at  'the  well-known  toy-shop  in  St.  James's  Street,' 
where  Sam  Johnson  smartened  himself  with  silver  buckles. 
(Boswell,  aet.  69).  He  would  not  have  the  ridiculous  large  ones 
in  fashion  ;  and  he  would  give  no  more  than  a  guinea  a  pair ; 
such,  says  Boswell,  in  Italics,  were  the  principles  of  the  business : 
and  I  think  this  may  be  the  first  place  in  which  the  philo- 
sophical word  was  brought  down  from  heaven  to  mix  with  men. 
However  this  may  be,  my  Wirgman  sold  snuff-boxes,  among 
other  things,  and  fifty  years  ago  a  fashionable  snuff-boxer  would 
be  under  inducement,  if  not  positively  obliged,  to  have  a  stock 
with  very  objectionable  pictures.  So  it  happened  that  Wirgman 
— by  reason  of  a  trifle  too  much  candour — came  under  the  notice 
of  the  Suppression  Society,  and  ran  considerable  risk.  Mr. 
Brougham  was  his  counsel ;  and  managed  to  get  him  acquitted. 
Years  and  years  after  this,  when  Mr.  Brougham  was  deep  in  the 
formation  of  the  London  University  (now  University  College), 
Mr.  Wirgman  called  on  him.  '  What  now  ?  '  said  Mr.  B.  with  his 
most  sarcastic  look — a  very  perfect  thing  of  its  kind — 'you're 
in  a  scrape  again,  I  suppose  ! '  '  No  !  indeed  ! '  said  W., '  my  present 
object  is  to  ask  your  interest  for  the  chair  of  Moral  Philosophy 
in  the  new  University  I '  He  had  taken  up  Kant ! 

Mr.  Wirgman,  an  itinerant  paradoxer,  called  on  me  in  1831 :  he 
came  to  convert  me.  '  I  assure  you,'  said  he,  '  I  am  nothing  but 
an  old  brute  of  a  jeweller  ; '  and  his  eye  and  manner  were  of  the 
extreme  of  jocosity,  as  good  in  their  way,  as  the  satire  of  his 
former  counsel.  I  mention  him  as  one  of  that  class  who  go  away 
quite  satisfied  that  they  have  wrought  conviction.  '  Now,'  said  he, 


154  A  BUDGET  OF  PABADOXES. 

'  I'll  make  it  clear  to  you !  Suppose  a  number  of  gold-fishes  in  a 
glass  bowl — you  understand  ?  Well !  I  come  with  my  cigar, 
and  go  puff,  puff,  puff,  over  the  bowl,  until  there  is  a  little  cloud 
of  smoke  :  now,  tell  me,  what  will  the  gold-fishes  say  to  that  ? ' 
'  I  should  imagine,'  said  I,  '  that  they  would  not  know  what  to  make 
of  it.'  '  By  Jove  !  you're  a  Kantian  ; '  said  he,  and  with  this  and 
the  like,  he  left  me,  vowing  that  it  was  delightful  to  talk  to  so 
intelligent  a  person.  The  greatest  compliment  Wirgman  ever 
received  was  from  James  Mill,  who  used  to  say  he  did  not  under- 
stand Kant.  That  such  a  man  as  Mill  should  think  this  worth 
saying  is  a  feather  in  the  cap  of  the  jocose  jeweller. 

Some  of  my  readers  will  stare  at  my  supposing  that  Boswell 
may  have  been  the  first  down-bringer  of  the  word  principles  into 
common  life ;  the  best  answer  will  be  a  prior  instance  of  the 
word  as  true  vernacular ;  it  has  never  happened  to  me  to  notice 
one.  Many  words  have  very  common  uses  which  are  not  old. 
Take  the  following  from  Nichols  (Anecd.  ix.  263) :  <  Lord 
Thurlow  presents  his  best  respects  to  Mr.  and  Mrs.  Thicknesse, 
and  assures  them  that  he  knows  of  no  cause  to  complain  of  any 
part  of  Mr.  Thicknesse's  carriage ;  least  of  all  the  circumstance  of 
sending  the  head  to  Ormond  Street.'  Surely  Mr.  T.  had  lent 
Lord  T.  a  satisfactory  carriage  with  a  moveable  head,  and  the 
above  is  a  polite  answer  to  inquiries.  Not  a  bit  of  it !  carriage 
is  here  conduct,  and  the  head  is  a  bust.  The  vehicles  of  the 
rich,  at  the  time,  were  coaches,  chariots,  chaises,  &c.,  never 
carriages,  which  were  rather  carts.  Gibbon  has  the  word  for 
baggage-waggons.  In  Jane  Austen's  novels  the  word  carriage  is 
established. 

John  Walsh,  of  Cork  (1786-1847).— This  discoverer  has  had 
the  honour  of  a  biography  from  Prof.  Boole,  who,  at  my  request, 
collected  information  about  him  on  the  scene  of  his  labours. 
It  is  in  the  Philosophical  Magazine  for  November,  1851,  and 
will,  I  hope,  be  transferred  to  some  biographical  collection  where 
it  may  find  a  larger  class  of  readers,  It  is  the  best  biography  of 
a  single  hero  of  the  kind  that  I  know.  Mr.  Walsh  introduced 
himself  to  me,  as  he  did  to  many  others,  in  the  anterowlandian 
days  of  the  Post-office ;  his  unpaid  letters  were  double,  treble, 
&c.  They  contained  his  pamphlets,  and  cost  their  weight  in 
silver  :  all  have  the  name  of  the  author,  and  all  are  in  octavo  or 
in  quarto  letter-form  :  most  are  in  four  pages,  and  all  dated  from 
Cork.  I  have  the  following  by  me  : — 


JOHN  WALSH'S  DELUSIONS.  155 


The  Geometric  Base.  1825.— The  theory  of  pl&ne  angles.  1827.— 
Three  Letters  to  Dr.  Francis  Sadleir.  1838. — The  invention  of 
polar  geometry.  By  Irelandus.  1839. — The  theory  of  partial 
functions.  Letter  to  Lord  Brougham.  1839. — On  the  invention 
of  polar  geometry.  1839. — Letter  to  the  Editor  of  the  Edin- 
burgh Review.  1840. — Irish  Manufacture.  A  new  method  of 
tangents.  1841. — The  normal  diameter  in  curves.  1843. — 
Letter  to  Sir  R.  Peel.  1845. — [Hints  that  Government  should 
compel  the  introduction  of  Walsh's  Geometry  into  Universities.] 
— Solution  of  Equations  of  the  higher  orders.  1845. 

Besides  these,  there  is  a  '  Metalogia,'  and  I  know  not  how  many 
others. 

Mr.  Boole,  who  has  taken  the  moral  and  social  features  of 
Walsh's  delusions  from  the  commiserating  point  of  view,  which 
makes  ridicule  out  of  place,  has  been  obliged  to  treat  Walsh  as 
Scott's  Alan  Fairford  treated  his  client  Peter  Peebles ;  namely, 
keep  the  scarecrow  out  of  court  while  his  case  was  argued.  My 
plan  requires  me  to  bring  him  in  :  and  when  he  comes  in  at  the 
door,  pity  and  sympathy  fly  out  at  the  window.  Let  the  reader 
remember  that  he  was  not  an  ignoramus  in  mathematics  :  he 
might  have  won  his  spurs  if  he  could  have  first  served  as  an 
esquire.  Though  so  illiterate  that  even  in  Ireland  he  never 
picked  up  anything  more  Latin  than  Irelandus,  he  was  a  very 
pretty  mathematician  spoiled  in  the  making  by  intense  self- 
opinion. 

This  is  part  of  a  private  letter  to  me  at  the  back  of  a  page  of 
print :  I  had  never  addressed  a  word  to  him  : — 

'  There  are  no  limits  in  mathematics,  and  those  that  assert  there  are, 
are  infinite  ruffians,  ignorant,  lying  blackguards.  There  is  no  dif- 
ferential calculus,  no  Taylor's  theorem,  no  calculus  of  variations,  &c. 
in  mathematics.  There  is  no  quackery  whatever  in  mathematics  ;  no 
$  equal  to  anything.  What  sheer  ignorant  blackguardism  that ! 

In  mechanics  the  parallelogram  of  forces  is  quackery,  and  is  danger- 
ous ;  for  nothing  is  at  rest,  or  in  uniform,  or  in  rectilinear  motion,  in 
the  universe.  Variable  motion  is  an  essential  property  of  matter. 
Laplace's  demonstration  of  the  parallelogram  of  forces  is  a  begging  of 
the  question ;  and  the  attempts  of  them  all  to  show  that  the  difference 
of  twenty  minutes  between  the  sidereal  and  actual  revolution  of  the 
earth  round  the  sun  arises  from  the  tugging  of  the  Sun  and  Moon  at 
the  pot-belly  of  the  earth,  without  being  sure  even  that  the  earth  has 
a  pot-belly  at  all,  is  perfect  quackery.  The  said  difference  arising 
from  and  demonstrating  the  revolution  of  the  Sun  itself  round  some 
distant  centre.' 


156  A  BUDGET  OF  PARADOXES. 

In  the  letter  to  Lord  Brougham  we  read  as  follows  : — 
'  I  ask  the  Royal  Society  of  London,  I  ask  the  Saxon  crew  of  that 
crazy  hulk,  where  is  the  dogma  of  their  philosophic  god  now  ?  .  .  . 
When  the  Royal  Society  of  London,  and  the  Academy  of  Sciences  of 
Paris,  shall  have  read  this  memorandum,  how  will  they  appear  ?  Like 
two  cur  dogs  in  the  paws  of  the  noblest  beast  of  the  forest  .  .  .  Just 
as  this  note  was  going  to  press,  a  volume  lately  published  by  you  was 
put  into  my  hands,  wherein  you  attempt  to  defend  the  fluxions  and 
Principia  of  Newton.  Man  !  what  are  you  about  ?  You  come  forward 
now  with  your  special  pleading,  and  fraught  with  national  prejudice, 
to  defend,  like  the  philosopher  Grassi,  the  persecutor  of  Galileo,  prin- 
ciples and  reasoning  which,  unless  you  are  actually  insane,  or  an 
ignorant  quack  in  mathematics,  you  know  are  mathematically  false. 
What  a  moral  lesson  this  for  the  students  of  the  University  of  London 
from  its  head  !  Man !  demonstrate  corollary  3,  in  this  note,  by  the 
lying  dogma  of  Newton,  or  turn  your  thoughts  to  something  you 
understand.' 

'WALSH  IEBLANDUS.' 

Mr.  Walsh — honour  to  his  memory — once  had  the  considera- 
tion to  save  me  postage  by  addressing  a  pamphlet  under  cover  to 
a  Member  of  Parliament,  with  an  explanatory  letter.  In  that 
letter  he  gives  a  candid  opinion  of  himself : — 

(1838.)  '  Mr.  Walsh  takes  leave  to  send  the  enclosed  corrected 
copy  to  Mr.  Hutton  as  one  of  the  Council  of  the  University  of  London, 
and  to  save  postage  for  the  Professor  of  Mathematics  there.  He  will 
find  in  it  geometry  more  deep  and  subtle,  and  at  the  same  time  more 
simple  and  elegant,  than  it  was  ever  contemplated  human  genius  could 
invent.' 

He  then  proceeds  to  set  forth  that  a  certain  '  tomfoolery 
lemma,'  with  its  '  tomfoolery '  superstructure,  *  never  had  exist- 
ence outside  the  shallow  brains  of  its  inventor,'  Euclid.  He  then 
proceeds  thus : — 

'  The  same  spirit  that  animated  those  philosophers  who  sent  Galileo 
to  the  Inquisition  animates  all  the  philosophers  of  the  present  day 
without  exception.  If  anything  can  free  them  from  the  yoke  of  error, 
it  is  the  [Walsh]  problem  of  double  tangence.  But  free  them  it  will, 
how  deeply  soever  they  may  be  sunk  into  mental  slavery — and  God 
knows  that  is  deeply  enough  ;  and  they  bear  it  with  an  admirable 
grace  ;  for  none  bear  slavery  with  a  better  grace  than  tyrants.  The 
lads  must  adopt  my  theory  ...  It  will  be  a  sad  reverse  for  all  our 
great  professors  to  be  compelled  to  become  schoolboys  in  their  gray 
years.  But  the  sore  scratch  is  to  be  compelled,  as  they  had  before 
been  compelled  one  thousand  years  ago,  to  have  recourse  to  Ireland 
for  instruction.' 


PROGRESS  OF  FREE  THOUGHT.  157 

The  following  '  Impromptu '  is  no  doubt  by  Walsh  himself:  he 
was  more  of  a  poet  than  of  an  astronomer  : — 

'  Through  ages  unfriended, 

With  sophistry  blended, 
Deep  science  in  Chaos  had  slept ; 

Its  limits  were  fettered, 

Its  voters  unlettered, 
Its  students  in  movements  but  crept. 

Till,  despite  of  great  foes, 

Great  WALSH  first  arose, 
And  with  logical  might  did  unravel 

Those  mazes  of  knowledge, 

Ne'er  known  in  a  college, 
Though  sought  for  with  unceasing  travail. 

With  cheers  we  now  hail  him, 

May  success  never  fail  him, 
In  Polar  Geometrical  mining ; 

Till  his  foes  be  as  tamed 

As  his  works  are  far-famed 
For  true  philosophic  refining.' 

Walsh's  system  is,  that  all  mathematics  and  physics  are  wrong : 
there  is  hardly  one  proposition  in  Euclid  which  is  demonstrated. 
His  example  ought  to  warn  all  who  rely  on  their  own  evidence  to 
their  own  success.  He  was  not,  properly  speaking,  insane ;  he 
only  spoke  his  mind  more  freely  than  many  others  of  his  class. 
The  poor  fellow  died  in  the  Cork  union,  during  the  famine.  He 
had  lived  a  happy  life,  contemplating  his  own  perfections,  like 
Brahma  on  the  lotos-leaf. 

The  year  1825  brings  me  to  about  the  middle  of  my  Athe- 
naeum list :  that  is,  so  far  as  mere  number  of  names  mentioned 
is  concerned.  Freedom  of  opinion,  beyond  a  doubt,  is  gaining 
ground,  for  good  or  for  evil,  according  to  what  the  speaker 
happens  to  think :  admission  of  authority  is  no  longer  made  in 
the  old  way.  If  we  take  soul-cure  and  body-cure,  divinity  and 
medicine,  it  is  manifest  that  a  change  has  come  over  us.  Time 
was  when  it  was  enough  that  dose  or  dogma  should  be  certified 
by  '  II  a  ete  ordonne,  Monsieur,  il  a  ete  ordonne,'  as  the  apothe- 
cary said  when  he  wanted  to  operate  upon  poor  de  Porceaugnac. 
Very  much  changed :  but  whether  for  good  or  for  evil  does  not 
now  matter  ;  the  question  is,  whether  contempt  of  demonstration 
such  as  our  paradoxers  show  has  augmented  with  the  rejection  of 
dogmatic  authority.  It  ought  to  be  just  the  other  way  :  for  the 


158  A  BUDGET  OF  PARADOXES. 

worship  of  reason  is  the  system  on  which,  if  we  trust  them,  the 
deniers  of  guidance  ground  their  plan  of  life.  The  following 
attempt  at  an  experiment  on  this  point  is  the  best  which  I  can 
make ;  and,  so  far  as  I  know,  the  first  that  ever  was  made. 

Say  that  my  list  of  paradoxers  divides  in  1825 :  this  of  itself 
proves  nothing,  because  so  many  of  the  earlier  books  are  lost,  or 
not  likely  to  be  come  at.  It  would  be  a  fearful  rate  of  increase 
which  would  make  the  number  of  paradoxes  since  1825  equal  to 
the  whole  number  before  that  date.  Let  us  turn  now  to  another 
collection  of  mine,  arithmetical  books,  of  which  I  have  published 
a  list.  The  two  collections  are  similarly  circumstanced  as  to 
new  and  old  books ;  the  paradoxes  had  no  care  given  to  the 
collection  of  either  ;  the  arithmetical  books  equal  care  to  both. 
The  list  of  arithmetical  books,  published  in  1847,  divides  at 
1735 ;  the  paradoxes,  up  to  1863,  divide  at  1825.  If  we  take 
the  process  which  is  most  against  the  distinction,  and  allow  every 
year  from  1847  to  1863  to  add  a  year  to  1735,  we  should  say 
that  the  arithmetical  writers  divide  at  1751.  This  rough  pro- 
cess may  serve,  with  sufficient  certainty,  to  show  that  the  pro- 
portion of  paradoxes  to  books  of  sober  demonstration  is  on  the 
increase ;  and  probably,  quite  as  much  as  the  proportion  of 
heterodoxes  to  books  of  orthodox  adherence.  So  that  divinity 
and  medicine  may  say  to  geometry,  Don't  you  sneer :  if  ration- 
alism, homoeopathy,  and  their  congeners  are  on  the  rise  among 
us,  your  enemies  are  increasing  quite  as  fast.  But  geometry 
replies — Dear  friends,  content  yourselves  with  the  rational  in- 
ference that  the  rise  of  heterodoxy  within  your  pales  is  not 
conclusive  against  you,  taken  alone  ;  for  it  rises  at  the  same 
time  within  mine.  Store  within  your  garners  the  precious 
argument  that  you  are  not  proved  wrong  by  increase  of  dissent ; 
because  there  is  increase  of  dissent  against  exact  science.  But 
do  not  therefore  even  yourselves  to  me :  remember  that  you, 
Dame  Divinity,  have  inflicted  every  kind  of  penalty,  from  the 
stake  to  the  stocks,  in  aid  of  your  reasoning ;  remember  that 
you,  Mother  Medicine,  have,  not  many  years  ago  applied  to 
Parliament  for  increase  of  forcible  hindrance  of  antipharma- 
copoeal  drenches,  pills,  and  powders.  Who  ever  heard  of  my 
asking  the  legislature  to  fine  blundering  circle-squarers  ?  Ee- 
member  that  the  D  in  dogma  is  the  D  in  decay ;  but  the  D  in 
demonstration  is  the  D  in  durability. 

I  have  known  a  medical  man — a  young  one — who  was  seriously 
of  opinion  that  the  country  ought  to  be  divided  into  medical 
parishes,  with  a  practitioner  appointed  to  each,  and  a  penalty 


MEDICAL  REFOKM.  159 

for  calling  in  any  but  the  incumbent  curer.  How  should  people 
know  how  to  choose  ?  The  hair-dressers  once  petitioned  Par- 
liament for  an  act  to  compel  people  to  wear  wigs.  My  own 
opinion  is  of  the  opposite  extreme,  as  in  the  following  letter 
(Examiner ',  April  5,  1856)  ;  which,  to  my  surprise,  I  saw  reprinted 
in  a  medical  journal,  as  a  plan  not  absolutely  to  be  rejected. 
I  am  perfectly  satisfied  that  it  would  greatly  promote  true 
medical  orthodoxy,  the  predominance  of  well  educated  thinkers, 
and  the  development  of  their  desirable  differences. 

SIR.  The  Medical  Bill  and  the  medical  question  generally  is 
one  on  which  experience  would  teach,  if  people  would  be  taught. 

The  great  soul  question  took  three  hundred  years  to  settle  :  the 
little  body  question  might  be  settled  in  thirty  years,  if  the  deci- 
sions in  the  former  question  were  studied. 

Time  was  when  the  State  believed,  as  honestly  as  ever  it 
believed  anything,  that  it  might,  could,  and  should  find  out 
true  doctrine  for  the  poor  ignorant  community ;  to  which,  like 
a  worthy  honest  state,  it  added  would.  Accordingly,  by  the 
assistance  of  a  Church,  which  undertook  the  physic,  the  surgery, 
and  the  pharmacy  of  sound  doctrine  all  by  itself,  it  sent  forth 
its  legally  qualified  teachers  into  every  parish,  and  woe  to  the 
man  who  called  in  any  other.  They  burnt  that  man,  they 
whipped  him,  they  imprisoned  him,  they  did  everything  but  what 
was  Christian  to  him,  all  for  his  soul's  health  and  the  amendment 
of  his  excesses. 

But  men  would  not  submit.  To  the  argument  that  the  State 
was  a  father  to  the  ignorant,  they  replied  that  it  was  at  best  the 
ignorant  father  of  an  ignorant  son,  and  that  a  blind  man  could 
find  his  way  into  a  ditch  without  another  blind  man  to  help  him. 
And  when  the  State  said — But  here  we  have  the  Church,  which 
knows  all  about  it,  the  ignorant  community  declared  that  it  had 
a  right  to  judge  that  question,  and  that  it  would  judge  it.  It 
also  said  that  the  Church  was  never  one  thing  long,  and  that  it 
progressed,  on  the  whole,  rather  more  slowly  than  the  ignorant 
community. 

The  end  of  it  was,  in  this  country,  that  every  one  who  chose 
taught  all  who  chose  to  let  him  teach,  on  condition  only  of  an  open 
and  true  registration.  The  State  was  allowed  to  patronise  one 
particular  Church,  so  that  no  one  need  trouble  himself  to  choose 
a  pastor  from  the  mere  necessity  of  choosing.  But  every  church 
is  allowed  its  colleges,  its  studies,  its  diplomas  ;  and  every  man 
is  allowed  his  choice.  There  is  no  proof  that  our  souls  are 


160  A  BUDGET  OF  PARADOXES. 

worse  off  than  in  the  sixteenth  century ;  and,  judging  by  fruits, 
there  is  much  reason  to  hope  they  are  better  off. 

Now  the  little  body  question  is  a  perfect  parallel  to  the  great 
soul  question  in  all  its  circumstances.  The  only  things  in  which 
the  parallel  fails  are  the  following :  Every  one  who  believes  in  a 
future  state  sees  that  the  soul  question  is  incomparably  more 
important  than  the  body  question,  and  every  one  can  try  the 
body  question  by  experiment  to  a  larger  extent  than  the  soul 
question.  The  proverb,  which  always  has  a  spark  of  truth  at  the 
bottom,  says  that  every  man  of  forty  is  either  a  fool  or  a 
physician  ;  but  did  even  the  proverb  maker  ever  dare  to  say  that 
every  man  is  at  any  age  either  a  fool  or  a  fit  teacher  of  religion  ? 

Common  sense  points  out  the  following  settlement  of  the 
medical  question :  and  to  this  it  will  come  sooner  or  later. 

Let  every  man  who  chooses — subject  to  one  common  law  of 
manslaughter  for  all  the  crass  cases — doctor  the  bodies  of  all 
who  choose  to  trust  him,  and  recover  payment  according  to 
agreement  in  the  courts  of  law.  Provided  always  that  every 
person  practising  should  be  registered  at  a  moderate  fee  in  a 
register  to  be  republished  every  six  months. 

Let  the  register  give  the  name,  address,  and  asserted  Qualifica- 
tion of  each  candidate — as  licentiate,  or  doctor,  or  what  not,  of 
this  or  that  college,  hall,  university,  &c.,  home  or  foreign.  Let 
it  be  competent  to  any  man  to  describe  himself  as  qualified  by 
study  in  public  schools  without  a  diploma,  or  by  private  study, 
or  even  by  intuition  or  divine  inspiration,  if  he  please.  But 
whatever  he  holds  his  qualification  to  be,  that  let  him  declare. 
Let  all  qualification  which  of  its  own  nature  admits  of  proof  be 
proved,  as  by  the  diploma  or  certificate,  &c.,  leaving  things  which 
cannot  be  proved,  as  asserted  private  study,  intuition,  inspiration, 
&c.,  to  work  their  own  way. 

Let  it  be  highly  penal  to  assert  to  the  patient  any  qualification 
which  is  not  in  the  register,  and  let  the  register  be  sold  very 
cheap.  Let  the  registrar  give  each  registered  practitioner  a  copy 
of  the  register  in  his  own  case ;  let  any  patient  have  power  to 
demand  a  sight  of  this  copy ;  and  let  no  money  for  attendance 
be  recoverable  in  any  case  in  which  there  has  been  false  repre- 
sentation. 

Let  any  party  in  any  suit  have  a  right  to  produce  what  medi- 
cal testimony  he  pleases.  Let  the  medical  witness  produce  his 
register,  and  let  his  evidence  be  for  the  jury,  as  is  that  of  an 
engineer  or  a  practitioner  of  any  art  which  is  not  attested  by 
diplomas. 


MEDICAL  REFORM—  REV.   R.   TAYLOR.  161 

Let  any  man  who  practises  without  venturing  to  put  his  name 
on  the  register  be  liable  to  fine  and  imprisonment. 

The  consequence  would  be  that,  as  now,  anybody  who  pleases 
might  practise  ;  for  the  medical  world  is  well  aware  that  there 
is  no  power  of  preventing  what  they  call  quacks  from  practising. 
But  very  different  from  what  is  now,  every  man  who  practises 
would  be  obliged  to  tell  the  whole  world  what  his  claim  is,  and 
would  run  a  great  risk  if  he  dared  to  tell  his  patient  in  private 
anything  different  from  what  he  had  told  the  whole  world. 

The  consequence  would  be  that  a  real  education  in  anatomy, 
physiology,  chemistry,  surgery,  and  what  is  known  of  the  thing 
called  medicine,  would  acquire  more  importance  than  it  now 
has. 

It  is  curious  to  see  how  completely  the  medical  man  of  the 
nineteenth  century  squares  with  the  priest  of  the  sixteenth  cen- 
tury. The  clergy  of  all  sects  are  now  better  divines  and  better 
men  than  they  ever  were.  They  have  lost  Bacon's  reproach  that 
they  took  a  smaller  measure  of  things  than  any  other  educated 
men  ;  and  the  physicians  are  now  in  this  particular  the  rear- 
guard of  the  learned  world  ;  though  it  may  be  true  that  the  rear 
in  our  day  is  further  on  in  the  march  than  the  van  of  Bacon's 
day.  Nor  will  they  ever  recover  the  lost  position  until  medicine 
is  as  free  as  religion. 

To  this  it  must  come.  To  this  the  public,  which  will  decide 
for  itself,  has  determined  it  shall  come.  To  this  the  public  has, 
in  fact,  brought  it,  but  on  a  plan  which  it  is  not  desirable  to 
make  permanent.  We  will  be  as  free  to  take  care  of  our  bodies 
as  of  our  souls  and  of  our  goods.  This  is  the  profession  of  all 
who  sign  as  I  do,  and  the  practice  of  most  of  those  who  would  not 
like  the  name  HETEROPATH.' 


The  motion  of  the  Sun  in  the  Ecliptic,  proved  to  be  uniform  in  a 
circular  orbit  .  .  .  with  preliminary  observations  on  the  fallacy 
of  the  Solar  System.  By  Bartholomew  Prescott,  1825,  8vo. 

The  author  had  published,  in  1803,  a  'Defence  of  the  Divine 
System,'  which  I  never  saw  ;  also,  '  On  the  inverted  scheme  of 
Copernicus.'  The  above  work  is  clever  in  its  satire. 

Manifesto  of  the  Christian  Evidence  Society,  established  Nov.  12, 
1824.  Twenty-four  plain  questions  to  honest  men. 

These  are  two  broadsides  of  August  and  November,  1826, 
signed  by  Robert  Taylor,  A.B.,  Orator  of  the  Christian  Evidence 


162  A  BUDGET  OF  PARADOXES. 

Society.  This  gentleman  was  a  clergyman,  and  was  convicted  of 
blasphemy  in  1827,  for  which  he  suffered  imprisonment,  and  got 
the  name  of  the  Devil's  Chaplain.  The  following  are  quota- 
tions :  — 

'  For  the  book  of  Revelation,  there  was  no  original  Greek  at  all,  but 
Erasmus  wrote  it  himself  in  Switzerland,  in  the  year  1516.  Bishop 
Marsh,  vol.  i.  p.  320.'- — '  Is  not  God  the  author  of  your  reason  ?  Can  he 
then  be  the  author  of  anything  which  is  contrary  to  your  reason  ?  If 
reason  be  a  sufficient  guide,  why  should  God  give  you  any  other  ?  if  it 
be  not  a  sufficient  guide,  why  has  he  given  you  that  ?  ' 

I  remember  a  votary  of  the  Society  being  asked  to  substitute  for 
reason  '  the  right  leg,'  and  for  guide  '  support,'  and  to  answer  the 
two  last  questions  :  he  said  there  must  be  a  quibble,  but  he  did 
not  see  what.  It  is  pleasant  to  reflect  that  the  argumentum  a, 
carcere  is  obsolete.  One  great  defect  of  it  was  that  it  did  not  go 
far  enough :  there  should  have  been  laws  against  subscriptions 
for  blasphemers,  against  dealing  at  their  shops,  and  against  rich 
widows  marrying  them. 

Had  I  taken  in  theology,  I  must  have  entered  books  against 
Christianity.  I  mention  the  above,  and  Paine's  '  Age  of  Reason,' 
simply  because  they  are  the  only  English  modern  works  that 
ever  came  in  my  way  without  my  asking  for  them.  The  three 
parts  of  the  '  Age  of  Reason '  were  published  in  Paris  1793,  Paris 
1795,  and  New  York  1807.  Carlile's  edition  is  of  London, 
1818,  8vo.  It  must  be  republished  when  the  time  comes,  to  show 
what  stuff  governments  and  clergy  were  afraid  of  at  the  begin- 
ning of  this  century.  I  should  never  have  seen  the  book,  if  it 
had  not  been  prohibited :  a  bookseller  put  it  under  my  nose  with 
a  fearful  look  round  him ;  and  I  could  do  no  less,  in  common 
curiosity,  than  buy  a  work  which  had  been  so  complimented  by 
church  and  state.  And  when  I  had  read  it,  I  said  in  my  mind  to 
church  and  state, — Confound  you  1  you  have  taken  me  in  worse 
than  any  reviewer  I  ever  met  with.  I  forget  what  I  gave  for 
the  book,  but  I  ought  to  have  been  able  to  claim  compensation 
somewhere. 


Cabbala  Algebraica.     Auctore  Gul.  Lud.  Christmann.  Stuttgard, 
1827,  4to. 

Eighty  closely  printed  pages  of  an  attempt  to  solve  equations 
of  every  degree,  which  has  a  process  called  by  the  author  cabbala. 
An  anonymous  correspondent  spells  cabbala  as  follows,  xaft/3a\\, 
and  makes  666  out  of  its  letters.  This  gentleman  has  sent  me, 


CABBALA   ALPHABETICA.  163 

since  my  Budget  commenced,  a  little  heap  of  satirical  communi- 
cations, each  having  a  666  or  two ;  for  instance,  alluding  to  my 
remarks  on  the  spelling  of  chemistry,  he  finds  the  fated  number  in 
^i/jLsia.  With  these  are  challenges  to  explain  them,  and  hints  about 
the  end  of  the  world.  All  these  letters  have  different  fantastic 
seals ;  one  of  them  with  the  legend  '  keep  your  temper,' — another 
bearing  *  bank  token  five  pence.'  The  only  signature  is  a  triangle 
with  a  little  circle  in  it,  which  I  interpret  to  mean  that  the 
writer  confesses  himself  to  be  the  round  man  stuck  in  the  three- 
cornered  hole,  to  be  explained  as  in  Sydney  Smith's  joke. 

There  is  a  kind  of  Cabbala  Alphabetica  which  the  investigators 
of  the  numerals  in  words  would  do  well  to  take  up :  it  is  the 
formation  of  sentences  which  contain  all  the  letters  of  the  alphabet, 
and  each  only  once.  No  one  has  done  it  with  v  and  j  treated  as 
consonants  ;  but  you  and  I  can  do  it.  Dr.  "Whewell  and  I  amused 
ourselves,  some  years  ago,  with  attempts.  He  could  not  make 
sense,  though  he  joined  words :  he  gave  me 

Phiz,  styx,  wrong,  buck,  flame,  quid. 

I  gave  him  the  following,  which  he  agreed  was  '  admirable 
sense  : '  I  certainly  think  the  words  would  never  have  come 
together  except  in  this  way : — 

I,  quartz  pyx,  who  fling  muck  beds. 

I  long  thought  that  no  human  being  could  say  this  under  any 
circumstances.  At  last  I  happened  to  be  reading  a  religious 
writer — as  he  thought  himself — who  threw  aspersions  on  his 
opponents  thick  and  threefold.  Heyday !  came  into  my  head, 
this  fellow  flings  muck  beds  ;  he  must  be  a  quartz  pyx.  And  then 
I  remembered  that  a  pyx  is  a  sacred  vessel,  and  quartz  is  a  hard 
stone,  as  hard  as  the  heart  of  a  religious  foe-curser.  So  that  the 
line  is  the  motto  of  the  ferocious  sectarian,  who  turns  his  religious 
vessels  into  mud-holders,  for  the  benefit  of  those  who  will  not 
see  what  he  sees. 

I    can    find    no    circumstances    for   the   following,   which    I 
received  from  another : — 

Fritz  !  quick  !  land  !  hew  gypsum  box. 
From  other  quarters  I  have  the  following  : — 
Dumpy  quiz  !  whirl  back  fogs  next. 

This  might  be  said  in  time  of  haze  to  the  queer  little  figure  in 


164  A  BUDGET   OF  PAKADOXES. 

the  Dutch  weather-toy,  which  comes  out  or  goes  in  with  the 
change  in  the  atmosphere.  Again, 

Export  my  fund !    Quiz  black  whigs. 

This  Squire  Western  might  have  said,  who  was  always  afraid  of 
the  whigs  sending  the  sinking-fund  over  to  Hanover.  But  the 
following  is  the  best :  it  is  good  advice  to  a  young  man,  very  well 
expressed  under  the  circumstances : — 

Get  nymph  ;  quiz  sad  brow  ;  fix  luck. 

"Which  in  more  sober  English  would  be,  Marry ;  be  cheerful ; 
watch  your  business.  There  is  more  edification,  more  religion  in 
this  than  in  all  the  666-interpretations  put  together. 

Such  things  would  make  excellent  writing  copies,  for  they 
secure  attention  to  every  letter ;  v  and  j  might  be  placed  at  the 
end. 

The  Celtic  Druids.    By  Godfrey  Higgins,  Esq.  of  Skellow  Grange, 

near  Doncaster.     London,  1827,  4to. 
Anacalypsis,  or  an  attempt  to  draw  aside  the  veil  of  the  Saitic 

Isis :  or  an  inquiry  into  the  origin  of  languages,  nations,  and 

religions.      By  Godfrey  Higgins,  &c London,  1836, 

2  vols.  4to. 

The  first  work  had  an  additional  preface  and  a  new  index  in 
1829.  Possibly,  in  future  time,  will  be  found  bound  up  with 
copies  of  the  second  work  two  sheets  which  Mr.  Higgins  circu- 
lated among  his  friends  in  1831 :  the  first  a  '  Eecapitulation,' the 
second  '  Book  vi.  ch.  1.' 

The  system  of  these  works  is  that — 

The  Buddhists  of  Upper  India  (of  whom  the  Phenician  Canaanite, 
Melchizedek,  was  a  priest),  who  built  the  Pyramids,  Stonehenge 
Carnac,  &c.  will  be  shown  to  have  founded  all  the  ancient  mythologies 
of  the  world,  which,  however  varied  and  corrupted  in  recent  times, 
were  originally  one,  and  that  one  founded  on  principles  sublime, 
beautiful,  and  true. 

These  works  contain  an  immense  quantity  of  learning,  very 
honestly  put  together.  I  presume  the  enormous  number  of  facts, 
and  the  goodness  of  the  index,  to  be  the  reasons  why  the  Ana- 
calypsis found  a  permanent  place  in  the  old  reading-room  of  the 
British  Museum,  even  before  the  change  which  greatly  increased 
the  number  of  books  left  free  to  the  reader  in  that  room. 

Mr.  Higgins,  whom  I  knew  well  in  the  last  six  years  of  his  life, 
and  respected  as  a  good,  learned,  and  (in  his  own  way) pious  man, 


GODFREY   HIGOINS.  165 

was  thoroughly  and  completely  the  man  of  a  system.  He  had 
that  sort  of  mental  connection  with  his  theory  that  made  his 
statements  of  his  authorities  trustworthy :  for,  besides  perfect 
integrity,  he  had  no  bias  towards  alteration  of  facts  :  he  saw  his 
system  in  the  way  the  fact  was  presented  to  him  by  his  authority, 
be  that  what  it  might. 

He  was  very  sure  of  a  fact  which  he  got  from  any  of  his 
authorities  :  nothing  could  shake  him.  Imagine  a  conversation 
between  him  and  an  Indian  officer  who  had  paid  long  attention 
to  Hindoo  antiquities  and  their  remains :  a  third  person  was 
present,  ego  qui  scribo.  G.  H.  'You  know  that  in  the  temples 
of  I-forget-who  the  Ceres  is  always  sculptured  precisely  as  in 

Greece.'  Col. ,  '  I  really  do  not  remember  it,  and  I  have 

seen  most  of  these  temples.'  G.  H.  '  It  is  so,  I  assure  you, 

especially  at  I-forget-where.'  Col. , 'Well,  I  am  sure!  I 

was  encamped  for  six  weeks  at  the  gate  of  that  very  temple,  and, 
except  a  little  shooting,  had  nothing  to  do  but  to  examine  its 
details,  which  I  did,  day  after  day,  and  I  found  nothing  of  the 
kind.'  It  was  of  no  use  at  all. 

Godfrey  Higgins  began  life  by  exposing  and  conquering,  at 
the  expense  of  two  years  of  his  studies,  some  shocking  abuses 
which  existed  in  the  York  Lunatic  Asylum.  This  was  a  pro- 
ceeding which  called  much  attention  to  the  treatment  of  the 
insane,  and  produced  much  good  effect.  He  was  very  resolute 
and  energetic.  The  magistracy  of  his  time  had  scruples  about 
using  the  severity  of  law  to  people  of  such  station  as  well-to-do 
farmers,  &c. :  they  would  allow  a  great  deal  of  resistance,  and 
endeavour  to  mollify  the  rebels  into  obedience.  A  young  farmer 
flatly  refused  to  pay  under  an  order  of  affiliation  made  upon  him 
by  Godfrey  Higgins.  He  was  duly  warned ;  and  persisted :  he 
shortly  found  himself  in  gaol.  He  went  there  sure  to  conquer 
the  Justice,  and  the  first  thing  he  did  was  to  demand  to  see  his 
lawyer.  He  was  told,  to  his  horror,  that  as  soon  as  he  had  been 
cropped  and  prison-dressed,  he  might  see  as  many  lawyers  as  he 
pleased,  to  be  looked  at,  laughed  at,  and  advised  that  there  was 
but  one  way  out  of  the  scrape.  Higgins  was,  in  his  speculations, 
a  regular  counterpart  of  Bailly  ;  but  the  celebrated  Mayor  of  Paris 
had  not  his  nerve.  It  is  impossible  to  say,  if  their  characters  had 
been  changed,  whether  the  unfortunate  crisis  in  which  Bailly  was 
not  equal  to  the  occasion  would  have  led  to  very  different  results 
if  Higgins  had  been  in  his  place :  but  assuredly  constitutional 
liberty  would  have  had  one  chance  more.  There  are  two  works 
of  his  by  which  he  was  known,  apart  from  his  paradoxes. 


166  A   BUDGET   OF   PARADOXES. 

First,  '  An  apology  for  the  life  and  character  of  the  celebrated 
prophet  of  Arabia,  called  Mohamed,  or  the  Illustrious.'  London, 
8vo.  1829.  The  reader  will  look  at  this  writing  of  our  English 
Buddhist  with  suspicious  eye,  but  he  will  not  be  able  to  avoid 
confessing  that  the  Arabian  prophet  has  some  reparation  to 
demand  at  the  hands  of  Christians.  Next,  '  Horse  Sabbaticse ;  or 
an  attempt  to  correct  certain  superstitions  and  vulgar  errors 
respecting  the  Sabbath.  Second  edition,  with  a  large  appendix.' 
London,  12mo.  1833.  This  book  was  very  heterodox  at  the 
time,  but  it  has  furnished  material  for  some  of  the  clergy  of  our 
day. 

I  never  could  quite  make  out  whether  Godfrey  Higgins  took 
that  system  which  he  traced  to  the  Buddhists  to  have  a  Divine 
origin,  or  to  be  the  result  of  good  men's  meditations.  Himself  a 
strong  theist,  and  believer  in  a  future  state,  one  would  suppose 
that  he  would  refer  a  universal  religion,  spread  in  different  forms 
over  the  whole  earth  from  one  source,  directly  to  the  universal 
Parent.  And  this  I  suspect  he  did,  whether  he  knew  it  or  not. 
The  external  evidence  is  balanced.  In  his  preface  he  says — 

*  I  cannot  help  smiling  when  I  consider  that  the  priests  Lave  objected 
to  admit  my  former  book,  "  the  Celtic  Druids,"  into  libraries,  because 
it  was  antichristian ;  and  it  has  been  attacked  by  Deists,  because  it 
•was  superfluously  religious.  The  learned  Deist,  the  Rev.  R.  Taylor 
[already  mentioned],  has  designated  me  as  tlie  religious  Mr.  Higgins.' 

The  time  will  come  when  some  profound  historian  of  literature 
will  make  himself  much  clearer  on  the  point  than  I  am. 

The  triumphal  Chariot  of  Friction  :  or  a  familiar  elucidation  of 
the  origin  of  magnetic  attraction,  &c.  &c.  By  William  Pope. 
London,  1829,  4to. 

Part  of  this  work  is  on  a  dipping-needle  of  the  author's  con- 
struction. It  must  have  been  under  the  impression  that  a  book 
of.  naval  magnetism  was  proposed,  that  a  great  many  officers,  the 
Royal  Naval  Club,  &c.  lent  their  names  to  the  subscription  list. 
How  must  they  have  been  surprised  to  find,  right  opposite  to  the 
list  of  subscribers,  the  plate  presenting  '  the  three  emphatic  letters, 
J.  A.  0.'  And  how  much  more  when  they  saw  it  set  forth  that  if 
a  square  be  inscribed  in  a  circle,  a  circle  within  that,  then  a 
square  again,  &c.,  it  is  impossible  to  have  more  than  fourteen 
circles,  let  the  first  circle  be  as  large  as  you  please.  From  this 
the  seven  attributes  of  Grod  are  unfolded ;  and  further,  that  all 
matter  was  moral,  until  Lucifer  churned  it  into  physical  '  as  far 


JACOTOT — TRACT  ON  PROBABILITY.  .    167 

as  the  third  circle  in  Deity ' :  this  Lucifer,  called  Leviathan  in 
Job,  being  thus  the  moving  cause  of  chaos.  I  shall  say  no  more, 
except  that  the  friction  of  the  air  is  the  cause  of  magnetism. 

Remarks  on  the  Architecture,  Sculpture,  and  Zodiac  of  Palmyra ; 
with  a  Key  to  the  Inscriptions.  By  B.  Prescot.  London, 
1830,  8vo. 

Mr.  Prescot  gives  the  signs  of  the  zodiac  a  Hebrew  origin. 

Epitome  de  matheinatiques.  Par  F.  Jacotot,  Avocat.  3ieme  edition. 

Paris,  1830,  8vo.  (pp.  18). 
Methode  Jacotot.      Choix  de  propositions  mathematiques.     Par 

P.  Y.  de  Sepres.     2nde  edition.     Paris,  1830,  8vo.  (pp.  82). 

Of  Jacotot's  method,  which  had  some  vogue  in  Paris,  the 
principle  was  Tout  est  dans  tout,  and  the  process  Apprendre 
quelque  chose,  et  a  y  rapporter  tout  le  reste.  The  first  tract  has 
a  proposition  in  conic  sections  and  its  preliminaries :  the  second 
has  twenty  exercises,  of  which  the  first  is  finding  the  greatest 
common  measure  of  two  numbers,  and  the  last  is  the  motion  of  a 
point  on  a  surface,  acted  on  by  given  forces.  This  is  topped  up 
with  the  problem  of  sound  in  a  tube,  and  a  slice  of  Laplac^s 
theory  of  the  tides.  All  to  be  studied  until  known  by  heart,  and 
all  the  rest  will  come,  or  at  least  join  on  easily  when  it  conies. 
There  is  much  truth  in  the  assertion  that  new  knowledge  hooks 
on  easily  to  a  little  of  the  old,  thoroughly  mastered.  The  day  is 
coming  when  it  will  be  found  out  that  crammed  erudition,  got  up 
for  examinations,  does  not  cast  out  any  hooks  for  more. 

Lettre  a  MM.  les  Membres  de  1'Academie  Boyale  des  Sciences, 
contenant  un  developpement  de  la  refutation  du  systeme  de  la 
gravitation  universelle,  qui  leur  a  etc  presentee  le  30  aout,  1830. 
Par  Felix  Passot.  Paris,  1830,  8vo. 

Works  of  this  sort  are  less  common  in  France  than  in  England. 
In  France  there  is  only  the  Academy  of  Sciences  to  go  to  :  in 
England  there  is  a  reading  public  out  of  the  Eoyal  Society,  &c. 

About  1830  was  published,  in  the  Librai^y  of  Useful  Know- 
ledge, the  tract  on  Probability,  the  joint  work  of  the  late  Sir 
John  Lubbock  and  Mr.  Driukwater  (Bethune).  It  is  one  of  the 
best  elementary  openings  of  the  subject.  A  binder  put  my  name 
on  the  outside  (the  work  was  anonymous)  and  the  consequence 
was  that  nothing  could  drive  out  of  people's  heads  that  it  was 


168  A  BUDGET   OF  PAKADOXES. 

written  by  me.  I  do  not  know  how  many  denials  I  have  made, 
from  a  passage  in  one  of  my  own  works  to  a  letter  in  the  Times : 
and  I  am  not  sure  that  I  have  succeeded  in  establishing  the 
truth,  even  now.  I  accordingly  note  the  fact  once  more.  But 
as  a  book  has  no  right  here  unless  it  contain  a  paradox — or  thing 
counter  to  general  opinion  or  practice — I  will  produce  two  small 
ones.  Sir  John  Lubbock,  with  whom  lay  the  executive  arrange- 
ment, had  a  strong  objection  to  the  last  word  in  '  Theory  of 
Probabilities,'  he  maintained  that  the  singular  probability,  should 
be  used  ;  and  I  hold  him  quite  right. 

The  second  case  was  this :  My  friend  Sir  J.  L.,  with  a  large 
cluster  of  intellectual  qualities,  and  another  of  social  qualities, 
had  one  point  of  character  which  I  will  not  call  bad  and  cannot 
call  good  ;  he  never  used  a  slang  expression.  To  such  a  length 
did  he  carry  his  dislike,  that  he  could  not  bear  head  and  tail, 
even  in  a  work  on  games  of  chance  :  so  he  used  obverse  and  reverse. 
I  stared  when  I  first  saw  this  :  but,  to  my  delight,  I  found  that 
the  force  of  circumstances  beat  him  at  last.  He  was  obliged  to 
take  an  example  from  the  race-course,  and  the  name  of  one  of 
the  horses  was  Bessy  Bedlam !  And  he  did  not  put  her  down  as 
Elizabeth  Bethlehem,  but  forced  himself  to  follow  the  jockeys. 
• 

[Almanach  Remain  sur  la  Loterie  Royale  de  France,  ou  les 
Utrennes  necessaires  aux  Actionnaires  et  Receveurs  de  la  dite 
Loterie.  Par  M.  Menut  de  St.-Mesmin.  Paris,  1830.  12mo. 

This  book  contains  all  the  drawings  of  the  French  lottery  (two 
or  three,  each  month)  from  1758  to  1830.  It  is  intended  for 
those  who  thought  they  could  predict  the  future  drawings  from 
the  past :  and  various  sets  of  sympathetic  numbers  are  given  to 
help  them.  The  principle  is,  that  anything  which  has  not 
happened  for  a  long  time  must  be  soon  to  come.  At  rouge  et 
noir,  for  example,  when  the  red  has  won  five  times  running, 
sagacious  gamblers  stake  on  the  black,  for  they  think  the  turn 
which  must  come  at  last  is  nearer  than  it  was.  So  it  is  :  but 
observation  would  have  shown  that  if  a  large  number  of  those 
cases  had  been  registered  which  show  a  run  of  five  for  the  red, 
the  next  game  would  just  as  often  have  made  the  run  into  six 
as  have  turned  in  favour  of  the  black.  But  the  gambling 
reasoner  is  incorrigible :  if  he  would  but  take  to  squaring  the 
circle,  what  a  load  of  misery  would  be  saved.  A  writer  of  1823, 
who  appeared  to  be  thoroughly  acquainted  with  the  gambling  of 
Paris  and  London,  says  that  the  gamesters  by  profession  are 
haunted  by  a  secret  foreboding  of  their  future  destruction,  and 


PAKADOXES  OF  CHANCE.  169 

seem  as  if  they  said  to  the  banker  at  the  table,  as  the  gladiators 
said  to  the  emperor,  Morituri  te  salutant. 

In  the  French  lottery,  five  numbers  out  of  ninety  were  drawn 
at  a  time.  Any  person,  in  any  part  of  the  country,  might  stake 
any  sum  upon  any  event  he  pleased,  as  that  27  should  be  drawn  ; 
that  42  and  81  should  be  drawn ;  that  42  and  81  should  be 
drawn,  and  42  first ;  and  so  on  up  to  a  quine  determine,  if  he 
chose,  which  is  betting  on  five  given  numbers  in  a  given  order. 
Thus,  in  July,  1821,  one  of  the  drawings  was 

8        46        16        64        13. 

A  gambler  had  actually  predicted  the  five  numbers  (but  not 
their  order),  and  won  131,350  francs  on  a  trifling  stake.  M. 
Menut  seems  to  insinuate  that  the  hint  what  numbers  to  cnoose 
was  given  at  his  own  office.  Another  won  20,852  francs  on  the 
quaterne  8,  16,  46,  64,. in  this  very  drawing.  These  gains,  of 
course,  were  widely  advertised :  of  the  multitudes  who  lost 
nothing  was  said.  The  enormous  number  of  those  who  played 
is  proved  to  all  who  have  studied  chances  arithmetically  by  the 
numbers  of  simple  quaternes  which  were  gained  :  in  1 822,  four- 
teen;  in  1823,  six  ;  in  1824,  sixteen;  in  1825,  nine,  &c. 

The  paradoxes  of  what  is  called  chance,  or  hazard,  might  them- 
selves make  a  small  volume.  All  the  world  understands  that 
there  is  a  long  run,  a  general  average ;  but  great  part  of  the 
world  is  surprised  that  this  general  average  should  be  computed 
and  predicted.  There  are  many  remarkable  cases  of  verification ; 
and  one  of  them  relates  to  the  quadrature  of  the  circle.  I  give 
some  account  of  this  and  another.  Throw  a  penny  time  after 
time  until  head  arrives,  which  it  will  do  before  long :  let  this 
be  called  a  set.  Accordingly,  H  is  the  smallest  set,  TH  the  next 
smallest,  then  TTH,  &c.  For  abbreviation,  let  a  set  in  which 
seven  tails  occur  before  head  turns  up  be  T7H.  In  an  immense 
number  of  trials  of  sets,  about  half  will  be  H ;  about  a  quarter 
TH;  about  an  eighth,  T2H.  Buffon  tried  2,048  sets;  and 
several  have  followed  him.  It  will  tend  to  illustrate  the  prin- 
ciple if  I  give  all  the  results ;  namely,  that  many  trials  will 
with  moral  certainty  show  an  approach — and  the  greater  the 
greater  the  number  of  trials — to  that  average  which  sober  reason- 
ing predicts.  In  the  first  column  is  the  most  likely  number  of 
the  theory :  the  next  column  gives  BufTon's  result ;  the  three 
next  are  results  obtained  from  trial  by  correspondents  of  mine. 
In  each  case  the  number  of  trials  is  2,048. 


170  A    BUDGET  OF  PAEADOXES. 


H 

1,024    . 

1,061     . 

1,048     .    1,017     . 

1,039 

TH      . 

512     . 

494     . 

507     . 

547    . 

480 

T2H    . 

256     . 

232     . 

248     . 

235     . 

267 

T'H    . 

128    . 

137    . 

99'   , 

118    . 

126 

T<H    . 

64    . 

56     . 

71    . 

72    -. 

67 

T5H    . 

32    . 

29     . 

38    . 

32    . 

33 

T6H    . 

16     . 

.    25     . 

17    . 

30    . 

19 

T7H    , 

8     . 

8    . 

9     . 

9    . 

10 

T8H    . 

4    . 

6    . 

,      5     . 

3     . 

3 

T9H    . 

2     . 

3    . 

2     . 

4 

Tl°H   . 

1     . 

1     . 

1 

TnH 

0     . 

1 

T12H 

0    . 

0 

T13H 

1     . 

1     . 

0 

TuH 

0    . 

0 

T15H 

1   . 

1 

&c. 

0 

0 

2,048     .    2,048     .    2,048     .    2,048     .    2,048 

In  very  many  trials,  then,  we  may  depend  upon  something  like 
the  predicted  average.  Conversely,  from  many  trials  we  may 
form  a  guess  at  what  the  average  will  be.  Thus,  in  Buffon's 
experiment  the  2,048  first  throws  of  the  sets  gave  head  in  1,061 
cases :  we  have  a  right  to  infer  that  in  the  long  run  something 
like  1,061  out  of  2,048  is  the  proportion  of  heads,  even  before 
we  know  the  reasons  for  the  equality  of  chance,  which  tell  us  that 
1,024  out  of  2,048  is  the  real  truth.  I  now  come  to  the  way  in 
which  such  considerations  have  led  to  a  mode  in  which  mere 
pitch-and-toss  has  given  a  more  accurate  approach  to  the  quadra- 
ture of  the  circle  than  has  been  reached  by  some  of  my  para- 
doxers.  What  would  my  friend1  in  No.  14  have  said  to  this? 
The  method  is  as  follows :  Suppose  a  planked  floor  of  the  usual 
kind,  with  thin  visible  seams  between  the  planks.  Let  there  be 
a  thin  straight  rod,  or  wire,  not  so  long  as  the  breadth  of  the 
plank.  This  rod,  being  tossed  up  at  hazard,  will  either  fall  quite 
clear  of  the  seams,  or  will  lay  across  one  seam.  Now  BufFon, 
and  after  him  Laplace,  proved  the  following :  That  in  the  long 
run  the  fraction  of  the  whole  number  of  trials  in  which  a  seam 
is  intersected  will  be  the  fraction  which  twice  the  length  of  the 
rod  is  of  the  circumference  of  the  circle  having  the  breadth  of  a 
plank  for  its  diameter.  In  1855  Mr.  Ambrose  Smith,  of  Aber- 
deen, made  3,204  trials  with  a  rod  three-fifths  of  the  distance 
between  the  planks:  there  were  1,213  clear  intersections,  and 
1 1  contacts  on  which  it  was  difficult  to  decide.  Divide  these 

1  See  p.  172.     This  article  was  a  supplement  to  No.  14  in  the  Athen&um  Budget. 


THE  INTERMINABLE   FRACTION   TT.  171 

contacts  equally,  and  we  have  1,218^  to  3,204  for  the  ratio  of  6 
to  5?r,  presuming  that  the  greatness  of  the  number  of  trials  gives 
something  near  to  the  final  average,  or  result  in  the  long  run  : 
this  gives  7r=3'1553.  If  all  the  11  contacts  had  been  treated  as 
intersections,  the  result  would  have  been  77  =  3'  141  2,  exceedingly 
near.  A  pupil  of  mine  made  600  trials  with  a  rod  of  the  length 
between  the  seams,  and  got  ?r=3'137. 

This  method  will  hardly  be  believed  until  it  has  been  re- 
peated so  often  that  '  there  never  could  have  been  any  doubt 
about  it.' 

The  first  experiment  strongly  illustrates  a  truth  of  the  theory, 
well  confirmed  by  practice  :  whatever  can  happen  will  happen  if  we 
make  trials  enough.  Who  would  undertake  to  throw  tail  eight 
times  running?  Nevertheless,  in  the  8,192  sets  tail  8  times 
running  occurred  17  times  ;  9  times  running,  9  times  ;  10  times 
running,  twice;  11  times  and  13  times,  each  once;  and  15  times, 
twice.] 

1830.  The  celebrated  interminable  fraction  3-14159.  .  .  ,  which 
the  mathematician  calls  TT,  is  the  ratio  of  the  circumference  to 
the  diameter.  But  it  is  thousands  of  things  besides.  It  is  con- 
stantly turning  up  in  mathematics  :  and  if  arithmetic  and  algebra 
had  been  studied  without  geometry,  IT  must  have  come  in  some- 
how, though  at  what  stage  or  under  what  name  must  have 
depended  upon  the  casualties  of  algebraical  invention.  This  will 
readily  be  seen  when  it  is  stated  that  TT  is  nothing  but  four  times 
the  series 


ad  infinitum.  It  would  be  wonderful  if  so  simple  a  series  had 
but  one  kind  of  occurrence.  As  it  is,  our  trigonometry  being 
founded  on  the  circle,  TT  first  appears  as  the  ratio  stated.  If,  for 
instance,  a  deep  study  of  probable  fluctuation  from  the  average 
had  preceded  geometry,  TT  might  have  emerged  as  a  number 
perfectly  indispensable  in  such  problems  as  —  What  is  the  chance 
of  the  number  of  aces  lying  between  a  million  +  x  and  a  million 
—  x,  when  six  million  of  throws  are  made  with  a  die  ?  I  have  not 
gone  into  any  detail  of  all  those  cases  in  which  the  paradoxer 
finds  out,  by  his  unassisted  acumen,  that  results  of  mathematical 
investigation  cannot  be  :  in  fact,  this  discovery  is  only  an  accom- 
paniment, though  a  necessary  one,  of  his  paradoxical  statement  of 
that  which  must  be.  Logicians  are  beginning  to  see  that  the 
notion  of  horse  is  inseparably  connected  with  that  of  non-horse  : 
that  the  first  without  the  second  would  be  no  notion  at  all.  And 
it  is  clear  that  the  positive  affirmation  of  that  -which  contradicts 


172  A   BUDGET   OF  PAEADOXES. 

mathematical  demonstration  cannot  but  be  accompanied  by  a 
declaration,  mostly  overtly  made,  that  demonstration  is  false.  If 
the  mathematician  were  interested  in  punishing  this  indiscretion, 
he  could  make  his  denier  ridiculous  by  inventing  asserted  results 
which  would  completely  take  him  in. 

More  than  thirty  years  ago  I  had  a  friend,  now  long  gone,  who 
was  a  mathematician,  but  not  of  the  higher  branches :  he  was, 
inter  alia,  thoroughly  up  in  all  that  relates  to  mortality,  life 
assurance,  &c.  One  day,  explaining  to  him  how  it  should  be 
ascertained  what  the  chance  is  of  the  survivors  of  a  large  number 
of  persons  now  alive  lying  between  given  limits  of  number  at  the 
end  of  a  certain  time,  I  came,  of  course,  upon  the  introduction  of 
TT,  which  I  could  only  describe  as  the  ratio  of  the  circumference 
of  a  circle  to  its  diameter.  '  Oh,  my  dear  friend  !  that  must  be 
a  delusion ;  what  can  the  circle  have  to  do  with  the  numbers 
alive  at  the  end  of  a  given  time  ? ' — '  I  cannot  demonstrate  it  to 
you;  but  it  is  demonstrated.' — 'Oh!  stuff!  I  think  you  can 
prove  anything  with  your  differential  calculus  :  figment,  depend 
upon  it.'  I  said  no  more  ;  but,  a  few  days  afterwards,  I  went  to 
him  and  very  gravely  told  him  that  I  had  discovered  the  law  of 
human  mortality  in  the  Carlisle  Table,  of  which  he  thought  very 
highly.  I  told  him  that  the  law  was  involved  in  this  circum- 
stance. Take  the  table  of  expectation  of  life,  choose  any  age, 
take  its  expectation  and  make  the  nearest  integer  a  new  age,  do 
the  same  with  that,  and  so  on ;  begin  at  what  age  you  like,  you 
are  sure  to  end  at  the  place  where  the  age  past  is  equal,  or  most 
nearly  equal,  to  the  expectation  to  come.  '  You  don't  mean  that 
this  always  happens  ?  ' — '  Try  it.'  He  did  try,  again  and  again ; 
and  found  it  as  I  said.  '  This  is,  indeed,  a  curious  thing ;  this  is 
a  discovery.'  I  might  have  sent  him  about  trumpeting  the  law 
of  life  :  but  I  contented  myself  with  informing  him  that  the  same 
thing  would  happen  with  any  table  whatsoever  in  which  the  first 
column  goes  up  and  the  second  goes  down  ;  and  that  if  a  pro- 
ficient in  the  higher  mathematics  chose  to  palm  a  figment  upon 
him,  he  could  do  without  the  circle  :  a  corsaire,  corsaire  et  demi, 
the  French  proverb  says.  'Oh  !'  it  was  remarked,  'I  see,  this  was 
Milne  ! '  It  was  not  Milne  :  I  remember  well  showing  the  formula 
to  him  some  time  afterwards.  He  raised  no  difficulty  about  TT  ; 
he  knew  the  forms  of  Laplace's  results,  and  he  was  much  "in- 
terested. Besides,  Milne  never  said  stuff !  and  figment !  And  he 
would  not  have  been  taken  in  :  he  would  have  quietly  tried  it 
with  the  Northampton  and  all  the  other  tables,  and  would  have 
grot  at  the  truth. 


EUCLID  WITHOUT   AXIOMS.  173 

The  first  book  of  Euclid's  Elements.  With  alterations  and 
familiar  notes.  Being  an  attempt  to  get  rid  of  axioms  alto- 
gether ;  and  to  establish  the  theory  of  parallel  lines,  without 
the  introduction  of  any  principle  not  common  to  other  parts  of 
the  elements.  By  a  member  of  the  University  of  Cambridge. 
Third  edition.  In  usum  serenissimje  filiolae.  London,  1830. 

The  author  was  Lieut. -Col.  (now  General)  Perronet  Thompson, 
the  author  of  the  '  Catechism  on  the  Corn  Laws.'  I  reviewed  the 
fourth  edition — which  had  the  name  of  '  Geometry  without 
Axioms,'  1833 — in  the  quarterly  Journal  of  Education  for 
January,  1834.  Col.  Thompson,  who  then  was  a  contributor  to — 
if  not  editor  of — the  Westminster  Review,  replied  in  an  article 
the  authorship  of  which  could  not  be  mistaken. 

Some  more  attempts  upon  the  problem,  by  the  same  author, 
will  be  found  in  the  sequel.  They  are  all  of  acute  and  legitimate 
speculation  ;  but  they  do  not  conquer  the  difficulty  in  the  manner 
demanded  by  the  conditions  of  the  problem.  The  paradox  of 
parallels  does  not  contribute  much  to  my  pages  :  its  cases  are  to 
be  found  for  the  most  part  in  geometrical  systems,  or  in  notes  to 
them.  Most  of  them  consist  in  the  proposal  of  additional  pos- 
tulates ;  some  are  attempts  to  do  without  any  new  postulate. 
Gen.  Perronet  Thompson,  whose  paradoxes  are  always  constructed 
on  much  study  of  previous  writers,  has  collected  in  the  work 
above-named,  a  budget  of  attempts,  the  heads  of  which  are  in  the 
Penny  and  English  Cyclopaedias,  at  '  Parallels.'  He  has  given 
thirty  instances,  selected  from  what  he  had  found. 

Lagrange,  in  one  of  the  later  years  of  his  life,  imagined  that  he 
had  overcome  the  difficulty.  He  went  so  far  as  to  write  a  paper, 
which  he  took  with  him  to  the  Institute,  and  began  to  read  it. 
But  in  the  first  paragraph  something  struck  him  which  he  had 
not  observed  :  he  muttered  II  faut  que  fy  songe  encore,  and  put 
the  paper  in  his  pocket. 


The  following  paragraph  appeared  in  the  Morning  Post, 
May  4,  1831  :— 

'  We  understand  that  although,  owing  to  circumstances  with  which 
the  public  are  uot  concerned,  Mr.  Groulburn  declined  becoming  a 
candidate  for  University  honours,  that  his  scientific  attainments  are 
far  from  inconsiderable.  He  is  well  known  to  be  the  author  of  an 
essay  in  the  Philosophical  Transactions  on  the  accurate  rectification  of 
a  circular  arc,  and  of  an  investigation  of  the  equation  of  a  lunar 


174  A  BUDGET   OF  PARADOXES. 

caustic — a  problem  likely  to   become  of  great  use   in  nautical   as- 
tronomy.' 

This  hoax — which  would  probably  have  succeeded  with  any 
journal — was  palmed  upon  the  Morning  Post.,  which  supported 
Mr.  Goulburn,  by  some  Cambridge  wags  who  supported  Mr. 
Lubbock,  the  other  candidate  for  the  University  of  Cambridge. 
Putting  on  the  usual  concealment,  I  may  say  that  I  always  sus- 
pected Dr-nkw-t-r  B-th-n-  of  having  a  share  in  the  matter.  The 
skill  of  the  hoax  lies  in  avoiding  the  words  '  quadrature  of  the 
circle,'  which  all  know,  and  speaking  of  '  the  accurate  rectification 
of  a  circular  arc,'  which  all  do  not  know  for  its  synonyme.  The 
Morning  Post  next  day  gave  a  reproof  to  hoaxers  in  general, 
without  referring  to  any  particular  case.  It  must  be  added, 
that  although  there  are  caustics  in  mathematics,  there  is  no 
lunar  caustic. 

So  far  as  Mr.  Groulburn  was  concerned,  the  above  was  poetic 
justice.  He  was  the  minister  who,  in  the  old  time,  told  a  depu- 
tation from  the  Astronomical  Society  that  the  Government  '  did 
not  care  twopence  for  all  the  science  in  the  country.'  There  may 
be  some  still  alive  who  remember  this  :  I  heard  it  from  more  than 
one  of  those  who  were  present,  and  are  now  gone.  Matters  are 
much  changed.  I  was  thirty  years  in  office  at  the  Astronomical 
Society ;  and,  to  my  certain  knowledge,  every  Government  of  that 
period,  Whig  and  Tory,  showed  itself  ready  to  help  with  influence 
when  wanted,  and  with  money  whenever  there  was  an  answer  for 
the  House  of  Commons.  The  following  correction  subsequently 
appeared.  Referring  to  the  hoax  about  Mr.  Groulburn,  Messrs.  C. 
H.  and  Thompson  Cooper  have  corrected  an  error,  by  stating  that 
the  election  which  gave  rise  to  the  hoax  was  that  in  which  Messrs. 
Groulburn  and  Yates  Peel  defeated  Lord  Palmerston  and  Mr. 
Cavendish.  They  add  that  Mr.  Gunning,  the  well-known  Esquire 
Bedell  of  the  University,  attributed  the  hoax  to  the  late  Eev.  R. 
Sheepshanks,  to  whom,  they  state,  are  also  attributed  certain  clever 
fictitious  biographies — of  public  men,  as  I  understand  it — which 
were  palmed  upon  the  editor  of  the  Cambridge  Chronicle,  who 
never  suspected  their  genuineness  to  the  day  of  his  death.  Being 
in  most  confidential  intercourse  with  Mr.  Sheepshaaks,  both  at  the 
time  and  all  the  rest  of  his  life  (twenty-five  years),  and  never 
having  heard  him  allude  to  any  such  things— which  were  not  in 
his  line,  though  he  had  satirical  power  of  quite  another  kind — I 
feel  satisfied  he  had  nothing  to  do  with  them.  I  may  add  that 
others,  his  nearest  friends,  and  also  members  of  his  family,  never 


SCIENTIFIC   ELECTION   SQUIB.  175 

heard  him  allude  to  these  hoaxes  as  their  author,  and  disbelieve 
his  authorship  as  much  as  I  do  myself.  I  say  this  not  as  imputing 
any  blame  to  the  true  author,  such  hoaxes  being  fair  election 
jokes  in  all  time,  but  merely  to  put  the  saddle  off  the  wrong  horse, 
and  to  give  one  more  instance  of  the  insecurity  of  imputed 
authorship.  Had  Mr.  Sheepshanks  ever  told  me  that  he  had 
perpetrated  the  hoax,  I  should  have  had  no  hesitation  in  giving 
it  to  him.  I  consider  all  clever  election  squibs,  free  from  bitter- 
ness and  personal  imputation,  as  giving  the  multitude  good 
channels  for  the  vent  of  feelings  which  but  for  them  would  cer- 
tainly find  bad  ones. 

[  But  I  now  suspect  that  Mr.  Babbage  had  some  hand  in  the 
hoax.  He  gives  it  in  his  '  Passages,  &c.'  and  is  evidently  writing 
from  memory,  for  he  gives  the  wrong  year.  But  he  has  given  the 
paragraph,  though  not  accurately,  yet  with  such  a  recollection  of 
the  points  as  brings  suspicion  of  the  authorship  upon  him,  perhaps 
in  conjunction  with  D.  B.  Both  were  on  Cavendish's  committee. 
Mr.  Babbage  adds,  that  '  late  one  evening  a  cab  drove  up  in  hot 
haste  to  the  office  of  the  Morning  Post,  delivered  the  copy  as 
coming  from  Mr.  Gmilburn's  committee,  and  at  the  same  time 
ordered  fifty  extra  copies  of  the  Post  to  be  sent  next  morning  to 
their  committee-room.  I  think  the  man — the  only  one  I  ever 
heard  of — who  knew  all  about  the  cab  and  the  extra  copies  must 
have  known  more.] 

Demonville. — A  Frenchman's  Christian  name  is  his  own  secret, 
unless  there  be  two  of  the  surname.  M.  Demonville  is  a  very 
good  instance  of  the  difference  between  a  French  and  English 
discoverer.  In  England  there  is  a  public  to  listen  to  discoveries 
in  mathematical  subjects  made  without  mathematics :  a  public 
which  will  hear,  and  wonder,  and  think  it  possible  that  the  pre- 
tensions of  the  discoverer  have  some  foundation.  The  unnoticed 
man  may  possibly  be  right :  and  the  old  country-town  reputation 
which  I  once  heard  of,  attaching  to  a  man  who  *  had  written  a 
book  about  the  signs  of  the  zodiac  which  all  the  philosophers  in 
London  could  not  answer,'  is  fame  as  far  as  it  goes.  Accordingly, 
we  have  plenty  of  discoverers  who,  even  in  astronomy,  pronounce 
the  learned  in  error  because  of  mathematics.  In  France,  beyond 
the  sphere  of  influence  of  the  Academy  of  Sciences,  there  is  no 
one  to  cast  a  thought  upon  the  matter :  all  who  take  the  least 
interest  repose  entire  faith  in  the  Institute.  Hence  the  French 
discoverer  turns  all  his  thoughts  to  the  Institute,  and  looks  for 


176  A  BUDGET   OF  PARADOXES. 

his  only  hearing  in  that  quarter.  He  therefore  throws  no  slur 
upon  the  means  of  knowledge,  but  would  say,  with  M.  Demon- 
ville — '  A  1'egard  de  M.  Poisson,  j'envie  loyalement  la  millieme 
partie  de  ses  connaissances  mathematiques,  pour  prouver  mon 
systeme  d'astronomie  aux  plus  incredules.'  This  system  is  that 
the  only  bodies  of  our  system  are  the  earth,  the  sun,  and  the 
moon ;  all  the  others  being  illusions,  caused  by  reflexion  of  the 
sun  and  moon  from  the  ice  of  the  polar  regions.  In  mathematics, 
addition  and  subtraction  are  for  men  ;  multiplication  and  division, 
which  are  in  truth  creation  and  destruction,  are  prerogatives  of 
Deity.  But  nothing  multiplied  by  nothing  is  one.  M.  Demon- 
ville  obtained  an  introduction  to  William  the  Fourth,  who  desired 
the  opinion  of  the  Eoyal  Society  upon  his  system :  the  answer 
was  very  brief.  The  King  was  quite  right ;  so  was  the  Society  : 
the  fault  lay  with  those  who  advised  His  Majesty  on  a  matter 
they  knew  nothing  about.  The  writings  of  M.  Demonville  in  my 
possession  are  as  follows.  The  dates — which  were  only  on  covers 
torn  off  in  binding — were  about  1831-34  : — 

'  Petit  cours  d'astronomie'  followed  by  '  Sur  1'unite  mathematique.' 
— Principes  de  la  physique  de  la  creation  implicitement  admis  dans  la 
notice  sur  le  tonnerre  par  M.  Arago. — Question  de  longitude  sur 
mer. — Vrai  systeme  du  monde  (pp.  92).  Same  title,  four  pages,  small 
type.  Same  title,  four  pages,  addressed  to  the  British  Association. 
Same  title,  four  pages,  addressed  to  M.  Mathieu.  Same  title,  four 
pages,  on  M.  Bouvard's  report. — Resume  de  la  physique  de  la  crea- 
tion ;  troisieme  partie  du  vrai  systeme  du  monde. 

The  quadrature  of  the  circle  discovered,  by  Arthur  Parsey,  author 
of  the  'art  of  miniature  painting.'  Submitted  to  the  consider- 
ation of  the  Royal  Society,  on  whose  protection  the  author 
humbly  throws  himself.  London,  1832,  8vo. 

Mr. .Parsey  was  an  artist,  who  also  made  himself  conspicuous 
by  a  new  view  of  perspective.  Seeing  that  the  sides  of  a  tower, 
for  instance,  would  appear  to  meet  in  a  point  if  the  tower  were 
high  enough,  he  thought  that  these  sides  ought  to  slope  to  one 
another  in  the  picture.  On  this  theory  he  published  a  small 
work,  of  which  I  have  not  the  title,  with  a  Grecian  temple  in  the 
frontispiece,  stated,  if  I  remember  rightly,  to  be  the  first  picture 
which  had  ever  been  drawn  in  true  perspective.  Of  course  the 
building  looked  very  Egyptian,  with  its  sloping  sides.  The 
answer  to  his  notion  is  easy  enough.  What  is  called  the  picture 
is  not  the  picture  from  which  the  mind  takes  its  perception ;  that 
picture  is  on  the  retina.  The  intermediate  picture,  as  it  may  be 
called — the  human  artist's  work — is  itself  seen  perspectively.  If 


PERSPECTIVE — RITCHIE'S   GEOMETRY.  177 

the  tower  were  so  high  that  the  sides,  though  parallel,  appeared 
to  meet  in  a  point,  the  picture  must  also  be  so  high  that  the 
picture-sides,  though  parallel,  would  appear  to  meet  in  a  point. 
I  never  saw  this  answer  given,  though  I  have  seen  and  heard  the 
remarks  of  artists  on  Mr.  Parsey's  work.  I  am  inclined  to  think 
it  is  commonly  supposed  that  the  artist's  picture  is  the  represen- 
tation which  comes  before  the  mind :  this  is  not  true  ;  we  might 
as  well  say  the  same  of  the  object  itself.  In  July  1831,  reading 
an  article  on  squaring  the  circle,  and  finding  that  there  was  a 
difficulty,  he  set  to  work,  got  a  light  denied  to  all  the  mathe- 
maticians in — some  would  say  through — a  crack,  and  advertised 
in  the  Times  that  he  had  done  the  trick.  He  then  prepared  this 
work,  in  which,  those  who  read  it  will  see  how,  he  showed  that 

3*14159 should  be  3-0625.     He  might  have  found  out  his 

error  by  stepping  a  draughtsman's  circle  with  the  compasses. 

Perspective  has  not  had  many  paradoxes.  The  only  other  one 
I  remember  is  that  of  a  writer  on  perspective,  whose  -name  I 
forget,  and  whose  four  pages  I  do  not  possess.  He  circulated 
remarks  on  my  notes  on  the  subject,  published  in  the  Athencewm*, 
in  which  he  denies  that  the  stereographic  projection  is'  a  case  of 
perspective,  the  reason  being  that  the  whole  hemisphere  makes 
too  large  a  picture  for  the  eye  conveniently  to  grasp  at  once. 
That  is  to  say,  it  is  no  perspective  because  there  is  too  much 
perspective. 

Principles  of  Geometry  familiarly  illustrated.     By  the  Rev.  W. 

Ritchie,  LL.D.     London,  1833,  12mo. 
A  new  Exposition  of  the  system  of  Euclid's  Elements,  being  an 

attempt  to  establish  his  work  on  a  different  basis.     By  Alfred 

Day,  LL.D.     London,  1839,  12mo. 

These  works  belong  to  a  small  class  which  have  the  peculiarity 
of  insisting  that  in  the  general  propositions  of  geometry  a  propo- 
sition gives  its  converse :  that  'Every  B  is  A'  follows  from  'Every 
A  is  B.'  Dr.  Ritchie  says,  '  If  it  be  proved  that  the  equality  of 
two  of  the  angles  of  a  triangle  depends  essentially  upon  the 
equality  of  the  opposite  sides,  it  follows  that  the  equality  of  the 
opposite  sides  depends  essentially  on  the  equality  of  the  angles.' 
Dr.  Day  puts  it  as  follows  : — 

'  That  the  converses  of  Euclid,  so  called,  where  no  particular  limit- 
ation is  specified  or  implied  in  the  leading  proposition,  more  than  in 
the  converse,  must  be  necessarily  true ;  for  as  by  the  nature  of  the 
reasoning  the  leading  proposition  must  be  universally  true,  should  the 
converse  not  be  so,  it  cannot  be  so  universally,  but  has  uu  lea^t  all  tho 

N 


178  A  BUDGET  OF  PAKADOXES. 

exceptions  conveyed  in  the  leading  proposition,  and  the  case  is  therefore 
unadapted  to  geometric  reasoning  ;  or,  what  is  the  same  thing,  by  the 
very  nature  of  geometric  reasoning,  the  particular  exceptions  to  the 
extended  converse  must  be  identical  with  some  one  or  other  of  the 
cases  under  the  universal  affirmative  proposition  with  which  we  set 
forth,  which  is  absurd.' 

On  this  I  cannot  help  transferring  to  my  reader  the  words  of  the 
Pacha  when  he  orders  the  bastinado, — May  it  do  you  good !  A 
rational  study  of  logic  is  much  wanted  to  show  many  mathema- 
ticians, of  all  degrees  of  proficiency,  that  there  is  nothing  in  the 
reasoning  of  mathematics  which  differs  from  other  reasoning. 
Dr.  Day  repeated  his  argument  in  '  A  Treatise  on  Proportion/ 
London,  1840,  8vo.  Dr.  Ritchie  was  a  very  clear-headed  man. 
He  published,  in  1818,  a  work  on  arithmetic,  with  rational  ex- 
planations. This  was  too  early  for  such  an  improvement,  and 
nearly  the  whole  of  this  excellent  work  was  sold  as  waste  paper. 
His  elementary  introduction  to  the  Differential  Calculus  was 
drawn  up  while  he  was  learning  the  subject  late  in  life.  Books 
of  this  sort  are  often  very  effective  on  points  of  difficulty. 


Letter  to  the  Royal  Astronomical  Society  in  refutation  of  Mistaken 
Notions  held  in  common,  by  the  Society,  and  by  all  the  New- 
tonian philosophers.  By  Capt.  Forman,  R.N.  Shepton- Mallet, 
1833,  8vo. 

Capt.  Forman  wrote  against  the  whole  system  of  gravitation, 
and  got  no  notice.  He  then  wrote  to  Lord  Brougham,  Sir  J. 
Herschel,  and  others  I  suppose,  desiring  them  to  procure  notice 
of  his  books  in  the  reviews :  this  not  being  acceded  to,  he  wrote 
(in  print)  to  Lord  John  Russell  to  complain  of  their  '  dishonest ' 
conduct.  He  then  sent  a  manuscript  letter  to  the  Astronomical 
Society,  inviting  controversy :  he  was  answered  by  a  recommen- 
dation to  study  dynamics.  The  above  pamphlet  was  the  con- 
sequence, in  which,  calling  the  Council  of  the  Society  '  craven 
dunghill  cocks,'  he  set  them  right  about  their  doctrines.  From 
all  I  can  learn,  the  life  of  a  worthy  man  and  a  creditable  officer 
was  completely  embittered  by  his  want  of  power  to  see  that  no 
person  is  bound  in  reason  to  enter  into  controversy  with  every 
one  who  chooses  to  invite  him  to  the  field.  This  mistake  is  not 
peculiar  to  philosophers,  whether  of  orthodoxy  or  paradoxy;  a 
majority  of  educated  persons  imply,  by  their  modes  of  proceeding, 
that  no  one  has  a  right  to  any  opinion  which  he  is  not  prepared 
to  defend  against  all  comers. 


INSPIRED  PARADOXERS.  179 


David  and  Goliath,  or  an  attempt  to  prove  that  the  Newtonian 
system  of  Astronomy  is  directly  opposed  to  the  Scriptures. 
By  Wm.  Lauder,  Sen.,  Mere,  Wilts.  Mere,  1833,  12mo. 

Newton  is  Goliath;  Mr.  Lauder  is  David.  David  took  five 
pebbles ;  Mr.  Lauder  takes  five  arguments.  He  expects  oppo- 
sition ;  for  Paul  and  Jesus  both  met  with  it. 

Mr.  Lauder,  in  his  comparison,  seems  to  put  himself  in  the 
divinely  inspired  class.  This  would  not  be  a  fair  inference  in 
every  case  ;  but  we  know  not  what  to  think  when  we  remember 
that  a  tolerable  number  of  cyclometers  have  attributed  their 
knowledge  to  direct  revelation.  The  works  of  this  class  are  very 
scarce  ;  I  can  only  mention  one  or  two  from  Montucla.  Alphonso 
Cano  de  Molina,  in  the  last  century,  upset  all  Euclid,  ani  squared 
the  circle  upon  the  ruins;  he  found  a  follower,  Janson,  who 
translated  him  from  Spanish  into  Latin.  He  declared  that  he 
believed  in  Euclid,  until  God,  who  humbles  the  proud,  taught 
him  better.  One  Paul  Yvon,  called  from  his  estate  de  la  Leu, 
a  merchant  at  Eochelle,  supported  by  his  book-keeper,  M.  Pujos, 
and  a  Scotchman,  John  Dunbar,  solved  the  problem  by  divine 
grace,  in  a  manner  which  was  to  convert  all  Jews,  Infidels,  &c. 
There  seem  to  have  been  editions  of  his  work  in  1619  and  1628, 
and  a  controversial  'Examen'  in  1630,  by  Eobert  Sara.  There 
was  a  noted  discussion,  in  which  Mydorge,  Hardy,  and  others 
took  part  against  de  la  Leu.  I  cannot  find  this  name  either  in 
Lipenius  or  Murhard,  and  I  should  not  have  known  the  dates  if 
it  had  not  been  for  one  of  the  keenest  bibliographers  of  any  time, 
my  friend  Prince  Balthasar  Boncompagni,  who  is  trying  to  find 
copies  of  the  works,  and  has  managed  to  find  copies  of  the  titles. 
In  1750,  Henry  Sullamar,  an  Englishman,  squared  the  circle  by 
the  number  of  the  Beast :  he  published  a  pamphlet  every  two  or 
three  years ;  but  I  cannot  find  any  mention  of  him  in  English 
works.  In  France,  in  1753,  M.  de  Causans,  of  the  Guards,  cut  a 
circular  piece  of  turf,  squared  it,  and  deduced  original  sin  and 
the  Trinity.  He  found  out  that  the  circle  was  equal  to  the 
square  in  which  it  is  inscribed ;  and  he  offered  a  reward  for 
detection  of  any  error,  and  actually  deposited  10,000  francs  as 
earnest  of  300,000.  But  the  courts  would  not  allow  any  one  to 
recover. 

1834.  In  this  year  Sir  John  Herschel  set  up  his  telescope  at 
Feldhausen,  Cape  of  Good  Hope.  He  did  much  for  astronomy, 

N    2 


180  A  BUDGET  OF  PARADOXES. 

but  not  much  for  the  Budget  of  Paradoxes.  He  gives  me,  how- 
ever, the  following  story.  He  showed  a  resident  a  remarkable 
blood-red  star,  and  some  little  time  after  he  heard  of  a  sermon 
preached  in  those  parts  in  which  it  was  asserted  that  the  state- 
ments of  the  Bible  must  be  true,  for  that  Sir  J.  H.  had  seen  in  his 
telescope  '  the  very  place  where  wicked  people  go.' 

But  red  is  not  always  the  colour.  Sir  J.  Herschel  has  in  his 
possession  a  letter  written  to  his  father,  Sir  W.  H.,  dated  April 
3,  1787,  and  signed  '  Eliza  Cumyns,'  begging  to  know  if  any  of 
the  stars  be  indigo  in  colour,  '  because,  if  there  be,  I  think  it 
may  be  deemed  a  strong  conjectural  illustration  of  the  expression, 
so  often  used  by  our  Saviour  in  the  Holy  Gospels,  that  "  the 
disobedient  shall  be  cast  into  outer  darkness  ;  "  for  as  the  Almighty 
Being  can  doubtless  confine  any  of  his  creatures,  whether  cor- 
poreal or  spiritual,  to  what  part  of  his  creation  He  pleases,  if 
therefore  any  of  the  stars  (which  are  beyond  all  doubt  so  many 
suns  to  other  systems)  be  of  so  dark  a  colour  as  that  above 
mentioned,  they  may  be  calculated  to  give  the  most  insufferable 
heat  to  those  dolorous  systems  dependent  upon  them  (and  to 
reprobate  spirits  placed  there),  without  one  ray  of  cheerful  light ; 
and  may  therefore  be  the  scenes  of  future  punishments.'  This 
letter  is  addressed  to  Dr.  Heirschel  at  Slow.  Some  have  placed 
the  infernal  regions  inside  the  earth,  but  others  have  filled  this 
internal  cavity — for  cavity  they  will  have — with  refulgent  light, 
and  made  it  the  abode  of  the  blessed.  It  is  difficult  to  build 
without  knowing  the  number  to  be  provided  for.  A  friend  of 
mine  heard  the  following  (part)  dialogue  between  two  strong 
Scotch  Calvinists :  '  Noo !  hoo  manny  d'ye  thank  there  are  of 
the  alact  on  the  arth  at  this  moment  ?— Eh  I  mabbee  a  doozen — 
Hoot !  mon !  nae  so  mony  as  thot  1 ' 

1834.  From  1769  to  1834  the  Nautical  Almanac  was  pub- 
lished on  a  plan  which  gradually  fell  behind  what  was  wanted. 
In  1834  the  new  series  began,  under  a  new  superintendent  (Lieut. 
"W.  S.  Stratford).  There  had  been  a  long  scientific  controversy, 
which  would  not  be  generally  intelligible.  To  set  some  of  the 
points  before  the  reader,  I  reprint  a  cutting  which  I  have  by  me. 
It  is  from  the  Nautical  Magazine,  but  I  did  hear  that  some  had 
an  idea  that  it  was  in  the  Nautical  Almanac  itself.  It  certainly 
was  not,  and  I  feel  satisfied  the  Lords  of  the  Admiralty  would 
not  have  permitted  the  insertion  ;  they  are  never  in  advance  of 
their  age.  The  Almanac  for  1834  was  published  in  July  1833. 


COUNCIL  OF  THE  SOLAR  SYSTEM.  181 


THE  NEW   NAUTICAL  ALMANAC. — Extract  from  the  'Primum  Mobile,' 
and  '  Milky  Way  Gazette.'     Communicated  by  AEROLITE. 

A  meeting  of  the  different  bodies  composing  the  Solar  System 
was  this  day  held  at  the  Dragon's  Tail,  for  the  purpose  of  taking 
into  consideration  the  alterations  and  amendments  introduced 
into  the  New  Nautical  Almanac.  The  honourable  luminaries 
had  been  individually  summoned  by  fast-sailing  comets,  and 
there  was  a  remarkably  full  attendance.  Among  the  visitors  we 
observed  several  nebulas,  and  almost  all  the  stars  whose  proper 
motions  would  admit  of  their  being  present. 

The  SUN  was  unanimously  called  to  the  focus.  The  small 
planets  took  the  oaths,  and  their  places,  after  a  short  discussion, 
in  which  it  was  decided  that  the  places  should  be  those  of  the 
Almanac  itself,  with  leave  reserved  to  move  for  corrections. 

Petitions  were  presented  from  a  and  8  Ursae  Minoris,  com- 
plaining of  being  put  on  daily  duty,  and  praying  for  an  increase  of 
salary. — Laid  on  the  plane  of  the  ecliptic. 

The  trustees  of  the  eccentricity1  and  inclination  funds  re- 
ported a  balance  of  '00001  in  the  former,  and  a  deficit  of  0"'009 
in  the  latter.  This  announcement  caused  considerable  surprise, 
and  a  committee  was  moved  for,  to  ascertain  which  of  the  bodies 
had  more  or  less  than  his  share.  After  some  discussion,  in 
which  the  small  planets  offered  to  consent  to  a  reduction,  if 
necessary,  the  motion  was  carried. 

The  FOCAL  BODY  then  rose  to  address  the  meeting.  He  re- 
marked that  the  subject  on  which  they  were  assembled  was  one 
of  great  importance  to  the  routes  and  revolutions  of  the  heavenly 
bodies.  For  himself,  though  a  private  arrangement  between  two 
of  his  honourable  neighbours  (here  he  looked  hard  at  the  Earth 
and  Venus)  had  prevented  his  hitherto  paying  that  close  atten- 
tion to  the  predictions  of  the  Nautical  Almanac  which  he  de- 
clared he  always  had  wished  to  do ;  yet  he  felt  consoled  by 
knowing  that  the  conductors  of  that  work  had  every  disposition 
to  take  his  peculiar  circumstances  into  consideration.  He  de- 
clared that  he  had  never  passed  the  wires  of  a  transit  without 
deeply  feeling  his  inability  to  adapt  himself  to  the  present  state 
of  his  theory ;  a  feeling  which  he  was  afraid  had  sometimes  caused 
a  slight  tremor  in  his  limb.  Before  he  sat  down,  he  expressed  a 
hope  that  honourable  luminaries  would  refrain  as  much  as 
possible  from  eclipsing  each  other,  or  causing  mutual  perturba- 

1  See  Sir  J.  Herschel's  Astronomy,  p.  369. 


182  A   BUDGET  OF  PARADOXES. 

tions.     Indeed,  he  should  be  very  sorry  to  see  any  interruption  of 
the  harmony  of  the  spheres.     (Applause.) 

The  several  articles  of  the  New  Nautical  Almanac  were  then 
read  over  without  any  comment ;  only  we  observed  that  Saturn 
shook  Ms  ring  at  every  novelty,  and  Jupiter  gave  his  belt  a 
hitch,  and  winked  at  the  satellites  at  page  21  of  each  month. 

The  MOON  rose,  to  propose  a  resolution.  No  one,  he  said, 
would  be  surprised  at  his  bringing  this  matter  forward  in  the 
way  he  did,  when  it  was  considered  in  how  complete  and  satis- 
factory a  manner  his  motions  were  now  represented.  He  must 
own  he  had  trembled  when  the  Lords  of  the  Admiralty  dissolved 
the  Board  of  Longitude,  but  his  tranquillity  was  more  than  re- 
established by  the  adoption  of  the  new  system.  He  did  not 
know  but  that  any  little  assistance  he  could  give  in  Nautical 
Astronomy  was  becoming  of  less  and  less  value  every  day,  owing 
to  the  improvement  of  chronometers.  But  there  was  one  thing, 
of  which  nothing  could  deprive  him — he  meant  the  regulation  of 
the  tides.  And,  perhaps,  when  his  attention  was  not  occupied  by 
more  than  the  latter,  he  should  be  able  to  introduce  a  little 
more  regularity  into  the  phenomena.  (Here  the  honourable 
luminary  gave  a  sort  of  modest  libration,  which  convulsed  the 
meeting  with  laughter.)  They  might  laugh  at  his  natural 
infirmity  if  they  pleased,  but  he  could  assure  them  it  arose  only 
from  the  necessity  he  was  under,  when  young,  of  watching  the 
motions  of  his  worthy  primary.  He  then  moved  a  resolution 
highly  laudatory  of  the  alterations  which  appeared  in  the  New 
Nautical  Almanac. 

The  EARTH  rose,  to  second  the  motion.  His  honourable  satel- 
lite had  fully  expressed  his  opinions  on  the  subject.  He  joined 
his  honourable  friend  in  the  focus  in  wishing  to  pay  every 
attention  to  the  Nautical  Almanac,  but,  really,  when  so  impor- 
tant an  alteration  had  taken  place  in  his  magnetic  pole l  (hear) 
and  there  might,  for  aught  he  knew,  be  a  successful  attempt  to 
reach  his  pole  of  rotation,  he  thought  he  could  not  answer  for 
the  preservation  of  the  precession  in  its  present  state.  (Here 
the  hon.  luminary,  scratching  his  side,  exclaimed,  as  he  sat  down, 
4  More  steam-boats — confound  'em !') 

An  honourable  satellite  (whose  name  we  could  not  learn)  pro- 
posed that  the  resolution  should  be  immediately  despatched,  cor- 
rected for  refraction,  when  he  was  called  to  order  by  the  Focal 
Body,  who  reminded  him  that  it  was  contrary  to  the  moving 

1  Captain  Ross  had  just  stuck  a  bit  of  brass  there. 


COUNCIL  OF  THE  SOLAR   SYSTEM.  183 

orders  of  the  system  to  take  cognizance  of  what  passed  inside  the 
atmosphere  of  any  planet. 

SATURN  and  PALLAS  rose  together.  (Cries  of  '  New  member  ! ' 
and  the  former  gave  way.)  The  latter,  in  a  long  and  eloquent 
speech,  praised  the  liberality  with  which  he  and  his  colleagues  had 
at  length  been  relieved  from  astronomical  disqualifications.  He 
thought  that  it  was  contrary  to  the  spirit  of  the  laws  of  gravita- 
tion to  exclude  any  planet  from  office  on  account  of  the  eccen- 
tricity or  inclination  of  his  orbit.  Honourable  luminaries  need 
not  talk  of  the  want  of  convergency  of  his  series.  What  had 
they  to  do  with  any  private  arrangements  between  him  and  the 
general  equations  of  the  system  ?  (Murmurs  from  the  opposi- 
tion.) So  long  as  he  obeyed  the  laws  of  motion,  to  which  he  had 
that  day  taken  a  solemn  oath,  he  would  ask,  were  old  planets, 
which  were  now  so  well  known  that  nobody  trusted  them, 
to  .... 

The  FOCAL  BODY  said  he  was  sorry  to  break  the  continuity  of 
the  proceedings,  but  he  thought  that  remarks  upon  character, 
with  a  negative  sign,  would  introduce  differences  of  too  high  an 
order.  The  honourable  luminary  must  eliminate  the  expression 
which  he  had  brought  out,  in  finite  terms,  and  use  smaller  in- 
equalities in  future.  (Hear,  hear.) 

PALLAS  explained,  that  he  was  far  from  meaning  to  reflect  upon 
the  orbital  character  of  any  planet  present.  He  only  meant  to 
protest  against  being  judged  by  any  laws  but  those  of  gravitation, 
and  the  differential  calculus:  he  thought  it  most  unjust  that 
astronomers  should  prevent  the  small  planets  from  being  ob- 
served, and  then  reproach  them  with  the  imperfections  of  the 
tables,  which  were  the  result  of  their  own  narrow-minded  policy. 
(Cheers. ) 

SATURN  thought  that,  as  an  old  planet,  he  had  not  been 
treated  with  due  respect.  (Hear,  from  his  satellites.)  He  had 
long  foretold  the  wreck  of  the  system  from  the  friends  of  inno- 
vation. Why,  he  might  ask,  were  his  satellites  to  be  excluded, 
when  small  planets,  trumpery  comets,  which  could  not  keep  their 
mean  distances  (cries  of  oh !  oh  !),  double  stars,  with  graphical 
approximations,  and  such  obscure  riff-raff  of  the  heavens  (great 
uproar)  found  room  enough.  So  help  him  Arithmetic,  nothing 
could  come  of  it,  but  a  stoppage  of  all  revolution.  His  hon. 
friend  in  the  focus  might  smile,  for  he  would  be  a  gainer  by  such 
an  event ;  but  as  for  him  (Saturn),  he  had  something  to  lose, 
and  hon.  luminaries  well  knew  that,  whatever  they  might  think 
under  an  atmosphere,  above  it  continual  revolution  was  the  only 


184  A   BUDGET   OF  PARADOXES. 

way  of  preventing  perpetual  anarchy.  As  to  the  hon.  luminary 
who  had  risen  before  him,  he  was  not  surprised  at  his  remarks, 
for  he  had  invariably  observed  that  he  and  bis  colleagues  allowed 
themselves  too  much  latitude.  The  stability  of  the  system  re- 
quired that  they  should  be  brought  down,  and  he,  for  one,  would 
exert  all  his  powers  of  attraction  to  accomplish  that  end.  If 
other  bodies  would  cordially  unite  with  him,  particularly  his 
noble  friend  next  him,  than  whom  no  luminary  possessed  greater 
weight — 

JUPITER  rose  to  order.  He  conceived  his  noble  friend  had  no 
right  to  allude  to  him  in  that  manner,  and  was  much  surprised  at 
his  proposal,  considering  the  matters  which  remained  in  dispute 
between  them.  In  the  present  state  of  affairs,  he  would  take 
care  never  to  be  in  conjunction  with  his  hon.  neighbour  one 
moment  longer  than  he  could  help.  (Cries  of  '  Order,  order,  no 
long  inequalities,'  during  which  he  sat  down.) 

SATURN  proceeded  to  say,  that  he  did  not  know  till  then  that  a 
planet  with  a  ring  could  affront  one  who  had  only  a  belt,  by  pro- 
posing mutual  co-operation.  He  would  now  come  to  the  subject 
under  discussion.  He  should  think  meanly  of  his  hon.  col- 
leagues if  they  consented  to  bestow  their  approbation  upon  a 
mere  astronomical  production.  Had  they  forgotten  that  they 
once  were  considered  the  arbiters  of  fate,  and  the  prognosticators 
of  man's  destiny  ?  What  had  lost  them  that  proud  position  ? 
Was  it  not  the  infernal  march  of  intellect,  which,  after  having 
turned  the  earth  topsy-turvy,  was  now  disturbing  the  very 
universe.  For  himself  (others  might  do  as  they  pleased),  but  he 
stuck  to  the  venerable  Partridge,  and  the  Stationers'  Company, 
and  trusted  that  they  would  outlive  infidels  and  anarchists,  whether 
of  Astronomical  or  Diffusion  of  Knowledge  Societies.  (Cries  of 
oh!  oh!) 

MARS  said  he  had  been  told,  for  he  must  confess  he  had  not 
seen  the  work,  that  the  places  of  the  planets  were  given  for 
Sundays.  This,  he  must  be  allowed  to  say,  was  an  indecorum 
he  had  not  expected ;  and  he  was  convinced  the  Lords  of  the 
Admiralty  had  given  no  orders  to  that  effect.  He  hoped  this 
point  would  be  considered  in  the  measure  which  had  been  intro- 
duced in  another  place,  and  that  some  one  would  move  that  the 
prohibition  against  travelling  on  Sundays  extend  to  the  heavenly 
as  well  as  earthly  bodies. 

Several  of  the  stars  here  declared,  that  they  had  been  much 
annoyed  by  being  observed  on  Sunday  evenings,  during  the  hours 
of  divine  service. 


COUNCIL   OF   THE   SOLAE   SYSTEM.  185 

The  room  was  then  cleared  for  a  division,  but  we  are  unable  to 
state  what  took  place.  Several  comets-at-arms  were  sent  for,  and 
we  heard  rumours  of  a  personal  collision  having  taken  place 
between  two  luminaries  in  opposition.  We  were  afterwards  told, 
that  the  resolution  was  carried  by  a  majority,  and  the  luminaries 
elongated  at  2  h.  15  m.  33,41  s.  sidereal  time. 


*  * 
* 


It  is  reported,  but  we  hope  without  foundation,  that 
Saturn,  and  several  other  discontented  planets,  have  accepted  an 
invitation  from  Sirius  to  join  his  system,  on  the  most  liberal 
appointments.  We  believe  the  report  to  have  originated  in 
nothing  more  than  the  discovery  of  the  annual  parallax  of  Sirius 
from  the  orbit  of  Saturn  ;  but  we  may  safely  assure  our  readers 
that  no  steps  have  as  yet  been  taken  to  open  any  communica- 
tion. 

We  are  also  happy  to  state,  that  there  is  no  truth  in  the 
rumour  of  the  laws  of  gravitation  being  about  to  be  repealed. 
We  have  traced  this  report,  and  find  it  originated  with  a  gentle- 
man living  near  Bath  (Captain  Forman,  E.N.),  whose  name  we 
forbear  to  mention. 

A  great  excitement  has  been  observed  among  the  nebulae, 
visible  to  the  earth's  southern  hemisphere,  particularly  among 
those  which  have  not  yet  been  discovered  from  thence.  We  are 
at  a  loss  to  conjecture  the  cause,  but  we  shall  not  fail  to  report 
to  our  readers  the  news  of  any  movement  which  may  take  place. 
(Sir  J.  Herschel's  visit.  He  could  just  see  this  before  he  went 
out.) 

A  Treatise  on  the  Divine  System  of  the  Universe,  by  Captain 
Woodley,  B.N.,  and  as  demonstrated  by  his  Universal  Time- 
piece, and  universal  method  of  determining  a  ship's  longitude 
by  the  apparent  true  place  of  the  moon  ;  with  an  introduction 
refuting  the  solar  system  of  Copernicus,  the  Newtonian  philo- 
sophy, and  mathematics.  1834.  8vo. 

Description  of  the  Universal  Time-piece.     (4  pp.  12mo.) 

I  think  this  divine  system  was  published  several  years  before, 
and  was  republished  with  an  introduction  in  1834.  Capt. 
Woodley  was  very  sure  that  the  earth  does  not  move :  he  pointed 
out  to  me,  in  a  conversation  I  had  with  him,  something — I  forget 
what — in  the  motion  of  the  Great  Bear,  visible  to  any  eye,  which 
could  not  possibly  be  if  the  earth  moved.  He  was  exceedingly 
ignorant,  as  the  following  quotation  from  his  account  of  the  usual 
opinion  will  show  : — 


186  A   BUDGET   OF   PARADOXES. 

The  north  pole  of  the  Earth's  axis  deserts,  they  say,  the  north  star 
or  pole  of  the  Heavens,  at  the  rate  of  1°  in  71|  years  .  .  .  The  fact  is, 
nothing  can  be  more  certain  than  that  the  Stars  have  not  changed 
their  latitudes  or  decimations  one  degree  in  the  last  71  f  years. 

This  is  a  strong  specimen  of  a  class  of  men  by  whom  all  ac- 
cessible persons  who  have  made  any  name  in  science  are  hunted. 
It  is  a  pity  that  they  cannot  be  admitted  into  scientific  societies, 
and  allowed  fairly  to  state  their  cases,  and  stand  quiet  cross- 
examination,  being  kept  in  their  answers  very  close  to  the 
questions,  and  the  answers  written  down.  I  am  perfectly  satisfied 
that  if  one  meeting  in  the  year  were  devoted  to  the  hearing  of 
those  who  chose  to  come  forward  on  such  conditions,  much  good 
would  be  done.  But  I  strongly  suspect  few  would  come  forward 
at  first,  and  none  in  a  little  while  :  and  I  have  had  some  ex- 
perience of  the  method  I  recommend,  privately  tried.  Capt. 
Woodley  was  proposed,  a  little  after  1834,  as  a  Fellow  of  the 
Astronomical  Society ;  and,  not  caring  whether  he  moved  the  sun 
or  the  earth,  or  both — I  could  not  have  stood  neither — I  signed 
the  proposal.  I  always  had  a  sneaking  kindness  for  paradoxers, 
such  a  one,  perhaps,  as  Petit  Andre  had  for  his  lambs,  as  he  called 
them.  There  was  so  little  feeling  against  his  opinions,  that  he 
only  failed  by  a  fraction  of  a  ball.  Had  I  myself  voted,  he  would 
have  been  elected ;  but  being  engaged  in  conversation,  and  not 
having  heard  the  slightest  objection  to  him,  I  did  not  think  it 
worth  while  to  cross  the  room  for  the  purpose.  I  regretted  this 
at  the  time,  but  had  I  known  how  ignorant  he  was  I  should  not 
have  supported  him.  Probably  those  who  voted  against  him 
knew  more  of  his  books  than  I  then  did. 

I  remember  no  other  instance  of  exclusion  from  a  scientific 
society  on  the  ground  of  opinion,  eves,  if  this  be  one  ;  of  which  it 
may  be  that  ignorance  had  more  to  do  with  it  than  paradoxy. 
Mr.  Frend,  a  strong  anti-Newtonian,  was  a  Fellow  of  the  Astro- 
nomical Society,  and  for  some  years  in  the  Council.  Lieut. 
Kerigan  was  elected  to  the  Eoyal  Society  at  a  time  when  his 
proposers  must  have  known  that  his  immediate  object  was  to  put 
F.E.S.  on  the  title-page  of  a  work  against  the  tides.  To  give  all 
I  know,  I  may  add  that  the  editor  of  some  very  ignorant  bombast 
about  the  '  forehead  of  the  solar  sky,:  who  did  not  know  the 
difference  between  Bailly  and  Baily,  received  hints  which  induced 
him  to  withdraw  his  proposal  for  election  into  the  Astronomical 
Society.  But  this  was  an  act  of  kindness ;  for  if  he  had  seen  Mr. 
Baily  in  the  chair,  with  his  head  on,  he  might  have  been  political 
historian  enough  to  faint  away. 


FRANCIS  BAILY  —  FLAMSTEED.  187 


De  la  formation  des  Corps.     Par  Paul  Laurent.    Nancy,  1834,  8vo. 

Atoms,  and  ether,  and  ovules  or  eggs,  which  are  planets,  and 
their  eggs,  which  are  satellites.  These  speculators  can  create 
worlds,  in  which  they  cannot  be  refuted  ;  but  none  of  them  dare 
attack  the  problem  of  a  grain  of  wheat,  and  its  passage  from  a 
seed  to  a  plant,  bearing  scores  of  seeds  like  what  it  was  itself. 

An  account  of  the  Rev.  John  Flamsteed,  the  First  Astronomer- 
Royal  ...  By  Francis  Baily,  Esq.  London,  1835,  4to.  Supple- 
ment, London,  1837,  4to. 

My  friend  Francis  Baily  was  a  paradoxer :  he  brought  forward 
things  counter  to  universal  opinion.  That  Newton  was  impeccable 
in  every  point  was  the  national  creed ;  and  failings  of  temper  and 
conduct  would  have  been  utterly  disbelieved,  if  the  paradox  had 
not  come  supported  by  very  unusual  evidence.  Anybody  who 
impeached  Newton  on  existing  evidence  might  as  well  have  been 
squaring  the  circle,  for  any  attention  he  would  have  got.  About 
this  book  I  will  tell  a  story.  It  was  published  by  the  Admiralty 
for  distribution  ;  and  the  distribution  was  entrusted  to  Mr.  Baily. 
On  the  eve  of  its  appearance,  rumours  of  its  extraordinary  reve- 
lations got  about,  and  persons  of  influence  applied  to  the  Admiralty 
for  copies.  The  Lords  were  in  a  difficulty :  but  on  looking  at 
the  list  they  saw  names,  as  they  thought,  which  were  so  obscure 
that  they  had  a  right  to  assume  Mr.  Baily  had  included  persons 
who  had  no  claim  to  such  a  compliment  as  presentation  from  the 
Admiralty.  The  Secretary  requested  Mr.  Baily  to  call  upon  him. 
'Mr.  Baily,  my  Lords  are  inclined  to  think  that  some  of  the 
persons  in  this  list  are  perhaps  not  of  that  note  which  would 
justify  their  Lordships  in  presenting  this  work.' — '  To  whom  does 
your  observation  apply,  Mr.  Secretary  ? ' — '  Well,  now,  let  us 
examine  the  list ;  let  me  see ;  now, — now, — now, — come  I — here's 
Gauss — who's  Gauss  ?  ' — '  Gauss,  Mr.  Secretary,  is  the  oldest 
mathematician  now  living,  and  is  generally  thought  to  be  the 
greatest.' — '  0-o-oh  !  Well,  Mr.  Baily,  we  will  see  about  it,  and  I 
will  write  you  a  letter.'  The  letter  expressed  their  Lordships' 
perfect  satisfaction  with  the  list. 

There  was  a  controversy  about  the  revelations  made  in  this 
work ;  but  as  the  eccentric  anomalies  took  no  part  in  it,  there  is 
nothing  for  my  purpose.  The  following  valentine  from  Mrs. 
Flamsteed,  which  I  found  among  Baily's  papers,  illustrates  some 
of  the  points  : — 


188  A   BUDGET  OF  PAEADOXES. 


'3  Astronomers'  Row,  Paradise :  February  14,  1836. 

*  Dear  Sir, — I  suppose  you  hardly  expected  to  receive  a  letter  from 
me,  dated  from  this  place  ;  but  the  truth  is,  a  gentleman  from  our 
street  was  appointed  guardian  angel  to  the  American  Treaty,  in  which 
there  is  some  astronomical  question  about  boundaries.  He  has  got 
leave  to  go  back  to  fetch  some  instruments  which  he  left  behind,  and 
I  take  this  opportunity  of  making  your  acquaintance.  That  America 
has  become  a  wonderful  place  since  I  was  down  among  you  ;  you  have 
no  idea  how  grand  the  fire  at  New  York  looked  up  here.  Poor  dear 
Mr.  Flamsteed  does  not  know  I  am  writing  a  letter  to  a  gentleman  on 
Valentine's  day ;  he  is  walked  out  with  Sir  Isaac  Newton  (they  are 
pretty  good  friends  now,  though  they  do  squabble  a  little  sometimes) 
and  Sir  William  Herschel,  to  see  a  new  nebula.  Sir  Isaac  says  he 
can't  make  out  at  all  how  it  is  managed ;  and  I  am  sure  I  cannot  help 
him.  I  never  bothered  my  head  about  those  things  down  below,  and 
I  don't  intend  to  begin  here. 

I  have  just  received  the  news  of  your  having  written  a  book  about 
my  poor  dear  man.  It's  a  chance  that  I  heard  it  at  all ;  for  the  truth 
is,  the  scientific  gentlemen  are  somehow  or  other  become  so  wicked, 
and  go  so  little  to  church,  that  very  few  of  them  are  considered  fit 
company  for  this  place.  If  it  had  not  been  for  Dr.  Brinkley,  who 
came  here  of  course,  I  should  not  have  heard  about  it.  He  seems  a 
nice  man,  but  is  not  yet  used  to  our  ways.  As  to  Mr.  Halley,  he  is  of 
course  not  here  ;  which  is  lucky  for  him,  for  Mr.  Flamsteed  swore  the 
moment  he  caught  him  in  a  place  where  there  are  no  magistrates,  he 
would  make  a  sacrifice  of  him  to  heavenly  truth.  It  was  very  generous 
in  Mr.  F.  not  appearing  against  Sir  Isaac  when  he  came  up,  for  I  am 
told  that  if  he  had,  Sir  Isaac  would  not  have  been  allowed  to  come  in 
at  all.  I  should  have  been  sorry  for  that,  for  he  is  a  companionable 
man  enough,  only  holds  his  head  rather  higher  than  he  should  do.  I 
met  him  the  other  pay  walking  with  Mr.  Whiston,  and  disputing  about 
the  deluge.  "  Well,  Mrs.  Flamsteed,"  says  he,  "  does  old  Poke-the- 
Stars  understand  gravitation  yet  ?  "  Now  you  must  know'that  is  rather 
a  sore  point  with  poor  dear  Mr.  Flamsteed.  He  says  that  Sir  Isaac  is 
as  crochetty  about  the  moon  as  ever  ;  and  as  to  what  some  people  say 
about  what  has  been  done  since  his  time,  he  says  he  should  like  to  see 
somebody  who  knows  something  about  it  of  himself.  For  it  is  very 
singular  that  none  of  the  people  who  have  carried  on  Sir  Isaac's  notions 
have  been  allowed  to  come  here. 

I  hope  you  have  not  forgotten  to  tell  how  badly  Sir  Isaac  used 
Mr.  Flamsteed  about  that  book.  I  have  never  quite  forgiven  him  ;  as 
for  Mr.  Flamsteed,  he  says  that  as  long  as  he  does  not  come  for  ob- 
servations, he  does  not  care  about  it,  and  that  he  will  never  trust  him 
with  any  papers  again  as  long  as  he  lives.  I  shall  never  forget  what 
a  rage  he  came  home  in  when  Sir  Isaac  had  called  him  a  puppy.  He 
struck  the  stairs  all  the  way  up  with  his  crutch,  and  said  puppy  at 


MRS.  FLAMSTE ED'S   VALENTINE.  189 

every  step,  and  all  the  evening,  as  soon  as  ever  a  star  appeared  in  the 
telescope,  he  called  it  puppy.  I  could  not  think  what  was  the  matter, 
and  when  I  asked,  he  only  called  me  puppy. 

I  shall  be  very  glad  to  see  you  if  you  come  our  way,  Pray  keep  up 
some  appearances,  and  go  to  church  a  little.  St.  Peter  is  always 
uncommonly  civil  to  astronomers,  and  indeed  to  all  scientific  persons, 
and  never  bothers  them  with  many  questions.  If  they  can  make  any- 
thing out  of  a  case,  he  is  sure  to  let  them  in.  Indeed,  he  says,  it  is 
perfectly  out  of  the  question  expecting  a  mathematician  to  be  as 
religious  as  an  apostle,  but  that  it  is  as  much  as  his  place  is  worth  to 
let  in  the  greater  number  of  those  who  come.  So  try  if  yon  cannot 
manage  it,  for  I  am  very  curious  to  know  whether  you  found  all  the 
letters.  I  remain,  dear  sir,  your  faithful  servant, 

MARGARET  FLAMSTEED. 

Francis  Baily,  Esq. 

P.S.  Mr.  Flamsteed  has  come  in,  and  says  he  left  Sir  Isaac  riding 
cockhorse  upon  the  nebula,  and  poring  over  it  as  if  it  were  a  book. 
He  has  brought  in  his  old  acquaintance  Ozanam,  who  says  that  it  was 
always  his  maxim  on  earth,  that  "  il  appartient  aux  docteurs  de 
Sorbonne  de  disputer,  au  Pape  de  prononcer,  et  au  mathematicien 
d'aller  en  Paradis  en  ligne  perpendiculaire." ' 

The  Secretary  of  the  Admiralty  was  completely  extinguished. 
I  can  recall  but  two  instances  of  demolition  as  complete,  though 
no  doubt  there  are  many  others.  The  first  is  in 

Simon  Stevin  and  M.  Dumortier.     Nieuport,  1845,  12mo. 

M.  Dumortier  was  a  member  of  the  Academy  of  Brussels  :  there 
was  a  discussion,  I  believe,  about  a  national  Pantheon  for  Bel- 
gium. The  name  of  Stevinus  suggested  itself  as  naturally  as 
that  of  Newton  to  an  Englishman  ;  probably  no  Belgian  is  better 
known  to  foreigners  as  illustrious  in  science.  Stevinus  is  great 
in  the  Mecanique  Analytique  of  Lagrange  ;  Stevinus  is  great  in 
the  Tristram,  Shandy  of  Sterne.  M.  Dumortier,  who  believed 
that  not  one  Belgian  in  a  thousand  knew  Stevinus,  and  who 
confesses  with  ironical  shame  that  he  was  not  the  odd  man, 
protested  against  placing  the  statue  of  an  obscure  man  in  the 
Pantheon,  to  give  foreigners  the  notion  that  Belgium  could  show 
nothing  greater.  Tbe  work  above  named  is  a  slashing  retort : 
any  one  who  knows  the  history  of  science  ever  so  little  may 
imagine  what  a  dressing  was  given,  by  mere  extract  from  foreign 
writers.  The  tract  is  a  letter  signed  J.  du  Fan,  but  this  is  a 
pseudonym  of  Mr.  Van  de  Weyer.  The  Academician  says 
Stevinus  was  a  man  who  was  not  without  merit  for  the  time  at 


190  A  BUDGET  OF  PARADOXES. 

which  he  lived :  Sir !  is  the  answer,  he  was  as  much  before  his 
own  time  as  you  are  behind  yours.  How  came  a  man  who 
had  never  heard  of  Stevinus  to  be  a  member  of  the  Brussels 
Academy  ? 

The  second  story  was  told  me  by  Mr.  Crabb  Eobinson,  who  was 
long  connected  with  the  Times,  and  intimately  acquainted  with 
Mr.  W***.  When  W***  was  an  undergraduate  at  Cambridge, 
taking  a  walk,  he  came  to  a  stile,  on  which  sat  a  bumpkin  who 
did  not  make  way  for  him :  the  gown  in  that  day  looked  down 
on  the  town.  '  Why  do  you  not  make  way  for  a  gentleman  ? ' 
— '  Eh  ? '  —  '  Yes,  why  do  you  not  move  ?  You  deserve  a  good 
hiding,  and  you  shall  get  it  if  you  don't  take  care  ? '  The 
bumpkin  raised  his  muscular  figure  on  its  feet,  patted  his 
menacer  on  the  head,  and  said,  very  quietly, — 'Young  man  !  I'm 
Cribb.'  W***  seized  the  great  pugilist's  hand,  and  shook  it 
warmly,  got  him  to  his  own  rooms  in  college,  collected  some 
friends,  and  had  a  symposium  which  lasted  until  the  large  end  of 
the  small  hours. 

God's  Creation  of  the  Universe  as  it  is,  in  support  of  the  Scriptures. 
By  Mr.  Finleyson.     Sixth  Edition,  1835,  8vo. 

This  writer,  by  his  own  account,  succeeded  in  delivering  the 
famous  Lieut.  Richard  Brothers  from  the  lunatic  asylum,  and 
tending  him,  not  as  a  keeper  but  as  a  disciple,  till  he  died. 
Brothers  was,  by  his  own  account,  the  nephew  of  the  Almighty, 
and  Finleyson  ought  to  have  been  the  nephew  of  Brothers.  For 
Napoleon  came  to  him  in  a  vision,  with  a  broken  sword  and  an 
arrow  in  his  side,  beseeching  help:  Finleyson  pulled  out  the 
arrow,  but  refused  to  give  a  new  sword ;  whereby  poor  Napoleon, 
though  he  got  off  with  life,  lost  the  battle  of  Waterloo.  This 
story  was  written  to  the  Duke  of  Wellington,  ending  with  '  I 
pulled  out  the  arrow,  but  left  the  broken  sword.  Your  Grace 
can  supply  the  rest,  and  what  followed  is  amply  recorded  in 
history.'  The  book  contains  a  long  account  of  applications  to 
Government  to  do  three  things  :  to  pay  2,000£.  for  care  taken  of 
Brothers,  to  pay  10,000£.  for  discovery  of  the  longitude,  and  to 
prohibit  the  teaching  of  the  Newtonian  system,  which  makes  God 
a  liar.  The  successive  administrations  were  threatened  that  they 
would  have  to  turn  out  if  they  refused,  which,  it  is  remarked, 
came  to  pass  in  every  case.  I  have  heard  of  a  joke  of  Lord 
Macaulay,  that  the  House  of  Commons  must  be  the  Beast  of  the 
Revelations,  since  658  members,  with  the  officers  necessary  for 
the  action  of  the  House,  make  666.  Macaulay  read  most  things, 


RICHARD   BROTHERS,   PROPHET   AND   POET.  101 

and  the  greater  part  of  the  rest :  so  that  he  might  be  suspected 
of  having  appropriated  as  a  joke  one  of  Finleyson's  serious  points 
— 'I  wrote  Earl  Grey  upon  the  13th  of  July,  1831,  informing 
him  that  his  Reform  Bill  could  not  be  carried,  as  it  reduced  the 
members  below  the  present  amount  of  658,  which,  with  the 
eight  principal  clerks  or  officers  of  the  House,  make  the  number 
666.'  But  a  witness  has  informed  me  that  Macaulay's  joke  was 
made  in  his  hearing  a  great  many  years  before  the  Reform  Bill 
was  proposed ;  in  fact,  when  both  were  students  at  Cambridge. 
Earl  Grey  was,  according  to  Finleyson,  a  descendant  of  Uriah 
the  Hittite.  For  a  specimen  of  Lieut.  Brothers,  this  book  would 
be  worth  picking  up.  Perhaps  a  specimen  of  the  Lieutenant's 
poetry  may  be  acceptable  :  Brothers  loquitur,  remember  : — 

Jerusalem  !  Jerusalem  !  shall  be  built  again  ! 

More  rich,  more  grand  than  ever  ; 
And  through  it  shall  Jordan  flow  !  (!) 

My  people's  favourite  river. 
There  I'll  erect  a  splendid  throne, 

And  build  on  the  wasted  place ; 
To  fulfil  my  ancient  covenant 

To  King  David  and  his  race. 
****** 

Euphrates'  stream  shall  flow  with  ships, 

And  also  my  wedded  Nile  ; 
And  on  my  coast  shall  cities  rise, 

Each  one  distant  but  a  mile. 

****** 

My  friends  the  Russians  on  the  north 

With  Persees  and  Arabs  round, 
Do  show  the  limits  of  my  land, 

Here  !  Here !  then  I  mark  the  ground. 

Among  the  paradoxers  are  some  of  the  theologians  who  in 
their  own  organs  of  the  press  venture  to  criticise  science.  These 
may  hold  their  ground  when  they  confine  themselves  to  the 
geology  of  long  past  periods  and  to  general  cosmogony  :  for  it  is 
the  tug  of  Greek  against  Greek ;  and  both  sides  deal  much  in 
what  is  grand  when  called  hypothesis,  petty  when  called  supposi- 
tion. And  very  often  they  are  not  conspicuous  when  they 
venture  upon  things  within  knowledge  ;  wrong,  but  not  quite 
wrong  enough  for  a  Budget  of  Paradoxes.  One  case,  however, 
is  destined  to  live,  as  an  instance  of  a  school  which  finds  writers, 
editors,  and  readers.  The  double  stars  have  been  seen  from  the 
seventeenth  century,  and  diligently  observed  by  many  from  the 


192  A  BUDGET  OF  PAEADOXES. 

time  of  Wm.  Herschel,  who  first  devoted  continuous  attention  to 
them.  The  year  1836  was  that  of  a  remarkable  triumph  of 
astronomical  prediction.  The  theory  of  gravitation  had  been 
applied  to  the  motion  of  binary  stars  about  each  other,  in  elliptic 
orbits,  and  in  that  year  the  two  stars  of  7  Virginis,  as  had  been 
predicted  should  happen  within  a  few  years  of  that  time — for 
years  are  small  quantities  in  such  long  revolutions — the  two 
stars  came  to  their  nearest :  in  fact,  they  appeared  to  be  one  as 
much  with  the  telescope  as  without  it.  This  remarkable  turn- 
ing-point of  the  history  of  a  long  and  widely-known  branch  of 
astronomy  was  followed  by  an  article  in  the  Church  of  England 
Quarterly  Review  for  April  1837,  written  against  the  Useful 
Knowledge  Society.  The  notion  that  there  are  any  such  things 
as  double  stars  is  (p.  460)  implied  to  be  imposture  or  delusion, 
as  in  the  following  extract.  I  suspect  that  I  myself  am  the 
Sidrophel,  and  that  my  companion  to  the  maps  of  the  stars, 
written  for  the  Society  and  published  in  1 836,  is  the  work  to 
which  the  writer  refers  : — 

We  have  forgotten  the  name  of  that  Sidrophel  who  lately  discovered 
that  the  fixed  stars  were  not  single  stars,  but  appear  in  the  heavens, 
like  soles  at  Billingsgate,  in  pairs ;  while  a  second  astronomer,  under 
the  influence  of  that  competition  in  trade  which  the  political  economists 
tell  us  is  so  advantageous  to  the  public,  professes  to  show  us,  through 
his  superior  telescope,  that  the  apparently  single  stars  are  really  three. 
Before  such  wondrous  mandarins  of  science,  how  continually  must 
homunculi  like  ourselves  keep  in  the  background,  lest  we  come  between 
the  wind  and  their  nobility. 

If  the  homunculus  who  wrote  this  be  still  above  ground,  how 
devoutly  must  he  hope  he  may  be  able  to  keep  in  the  back- 
ground !  But  the  chief  blame  falls  on  the  editor.  The  title  of 
the  article  is — 

The  new  school  of  superficial  pantology ;  a  speech  intended  to  be 
delivered  before  a  defunct  Mechanics'  Institute.  By  Swallow  Swift, 
late  M.P.  for  the  Borough,  of  Cockney- Cloud,  Witsbury :  reprinted 
Balloon  Island,  Bubble  year,  month  Ventose.  Long  live  Charlatan ! 

As  a  rule,  orthodox  theologians  should  avoid  humour,  a  weapon 
which  all  history  shows  to  be  very  difficult  to  employ  in  favour 
of  establishment,  and  which,  nine  times  out  of  ten,  leaves  its 
wielder  fighting  on  the  side  of  heterodoxy.  Theological  argu- 
ment, when  not  enlivened  by  bigotry,  is  seldom  worse  than 
narcotic  :  but  theological  fun,  when  not  covert  heresy,  is  almost 
always  sialagogue.  The  article  in  question  is  a  craze,  which  no 
editor  should  have  admitted,  except  after  severe  inspection  by 


SATIRICAL    CRITICISM.  193 

qualified  persons.  The  author  of  this  wit  committed  a  mistake 
which  occurs  now  and  then  in  old  satire,  the  confusion  between 
himself  and  the  party  aimed  at.  He  ought  to  be  reviewing  this 
fictitious  book,  but  every  now  and  then  the  article  becomes  the 
book  itself;  not  by  quotation,  but  by  the  writer  forgetting  that 
he  is  not  Mr.  Swallow  Swift,  but  his  reviewer.  In  fact,  he  and 
Mr.  S,  Swift  had  each  had  a  dose  of  the  Devil's  Elixir.  A  novel 
so  called,  published  about  forty  years  ago,  proceeds  upon  a 
legend  of  this  kind.  If  two  parties  both  drink  of  the  elixir, 
their  identities  get  curiously  intermingled  ;  each  turns  up  in 
the  character  of  the  other  throughout  the  three  volumes,  without 
having  his  ideas  clear  as  to  whether  he  be  himself  or  the  other. 
There  is  a  similar  confusion  in  the  answer  made  to  the  famous 
Epistolce  Obscurorum  Virorum:  it  is  headed  Lamentationes 
Obscurorum  Virorum.  This  is  not  a  retort  of  the  writer,  throw- 
ing back  the  imputation :  the  obscure  men  who  had  been 
satirized  are  themselves  made,  by  name,  to  wince  under  the 
disapprobation  which  the  Pope  had  expressed  at  the  satire  upon 
themselves. 

Of  course  the  book  here  reviewed  is  a  transparent  forgery. 
But  I  do  not  know  how  often  it  may  have  happened  that  the 
book,  in  the  journals  which  always  put  a  title  at  the  head,  may 
have  been  written  after  the  review.  About  the  year  1830  a 
friend  showed  me  the  proof  of  an  article  of  his  on  the  malt  tax, 
for  the  next  number  of  the  Edinburgh  Review.  Nothing  was 
wanting  except  the  title  of  the  book  reviewed ;  I  asked  what  it 
was.  He  sat  down,  and  wrote  as  follows  at  the  head,  '  The 
Maltster's  Guide  (pp.  124),'  and  said  that  would  do  as  well  as 
anything. 

But  I  myself,  it  will  be  remarked,  have  employed  such  humour 
as  I  can  command  'in  favour  of  establishment.'  What  it  is 
worth  I  am  not  to  judge ;  as  usual  in  such  cases,  those  who  are  of 
my  cabal  pronounce  it  good,  but  cyclometers  and  other  paradoxers 
either  call  it  very  poor,  or  commend  it  as  sheer  buffoonery.  Be 
it  one  or  the  other,  I  observe  that  all  the  effective  ridicule  is,  in 
this  subject,  on  the  side  of  establishment.  This  is  partly  due  to 
the  difficulty  of  quizzing  plain  and  sober  demonstration ;  but  so 
much,  if  not  more,  to  the  ignorance  of  the  paradoxers.  For  that 
which  cannot  be  ridiculed,  can  be  turned  into  ridicule  by  those 
who  know  how.  But  by  the  time  a  person  is  deep  enough  in 
negative  quantities,  and  impossible  quantities,  to  be  able  to  satirise 
them,  he  is^caught,  and  being  inclined  to  become  a  user,  sli rinks 
from  being  an  abuser.  Imagine  a  person  with  a  gift  of  ridicule, 

o 


194  A  BUDGET  OF  PARADOXES. 

and  knowledge  enough,  trying  his  hand  on  the  junction  of  the 
assertions  which  he  will  find  in  various  books  of  algebra.  First, 
that  a  negative  quantity  has  no  logarithm;  secondly,  that  a 
negative  quantity  has  no  square  root ;  thirdly,  that  the  first  non- 
existent is  to  the  second  as  the  circumference  of  a  circle  to  its 
diameter.  One  great  reason  of  the  allowance  of  such  unsound 
modes  of  expression  is  the  confidence  felt  by  the  writers  that  V— 1 
and  log  (-1)  will  make  their  way,  however  inaccurately  described. 
I  heartily  wish  that  the  cyclometers  had  knowledge  enough  to 
attack  the  weak  points  of  algebraical  diction  :  they  would  soon 
work  a  beneficial  change. 

Recueil  de  ma  vie,  mes  ouvrages  et  mes  pensees.     Par  Thomas 

Ignace  Marie  Forster.  Brussels,  1836,  12mo. 
Mr.  Forster,  an  Englishman  settled  at  Bruges,  was  an  observer 
in  many  subjects,  but  especially  in  meteorology.  He  communi- 
cated to  the  Astronomical  Society,  in  1848,  the  information  that, 
in  the  registers  kept  by  his  grandfather,  his  father,  and  himself, 
beginning  in  1767,  new  moon  on  Saturday  was  followed,  nineteen 
times  out  of  twenty,  by  twenty  days  of  rain  and  wind.  This 
statement  being  published  in  the  Athenceum,  a  cluster  of  corres- 
pondents averred  that  the  belief  is  common  among  seamen,  in  all 
parts  of  the  world,  and  among  landsmen  too.  Some  one  quoted 
a  distich — 

'  Saturday's  moon  and  Sunday's  full 
Never  were  fine  and  never  wull.' 
Another  brought  forward — 

'  If  a  Saturday's  moon 
Comes  once  in  seven  years  it  comes  too  soon.' 

Mr.  Forster  did  not  say  he  was  aware  of  the  proverbial  character 
of  the  phenomenon.  He  was  a  very  eccentric  man.  He  treated 
his  dogs  as  friends,  and  buried  them  with  ceremony.  He  quar- 
relled with  the  cure  of  his  parish,  who  remarked  that  he  could 
not  take  his  dogs  to  heaven  with  him.  I  will  go  nowhere,  said 
he,  where  I  cannot  take  my  dog.  He  was  a  sincere  Catholic :  but 
there  is  a  point  beyond  which  even  churches  have  no  influence. 

The  following  is  some  account  of  the  announcement  of  1849. 
The  Athenceum  (Feb.  17),  giving  an  account  of  the  meeting  of 
the  Astronomical  Society  in  December,  1858,  says: 

'  Dr.  Forster  of  Bruges,  who  is  well  known  as  a  meteorologist,  made 
a  communication  at  which  our  readers  will  stare  :  he  declares  that  by 
journals  of  the  weather  kept  by  his  grandfather,  father,  and  himself, 
ever  since  1767,  to  the  present  time,  whenever  the  new  moon  has  fallen 
on  a  Saturday i  the  following  twenty  days  have  been  wet  and  windy,  in 


A    SATURDAY'S    MOON.  195 

nineteen  cases  out  of  twenty.  In  spite  of  our  friend  Zadkiel  and  the 
others  who  declare  that  we  would  smother  every  truth  that  does  not 
happen  to  agree  with  us,  we  are  glad  to  see  that  the  Society  had 
the  sense  to  publish  this  communication,  coming,  as  it  does,  from  a 
veteran  observer,  and  one  whose  love  of  truth  is  undoubted.  It  must 
be  that  the  fact  is  so  set  down  in  the  journals,  because  Dr.  Forster 
says  it :  and  whether  it  be  only  a  fact  of  the  journals,  or  one  of  the 
heavens,  can  soon  be  tried.  The  new  moon  of  March  next,  falls  on 
Saturday  the  24th,  at  2  in  the  afternoon.  We  shall  certainly  look  out.' 

The  following  appeared  in  the  number  of  March  31  : — 

*  The  first  Saturday  Moon  since  Dr.  Forster's  announcement  came  off 
a  week  ago.  We  had  previously  received  a  number  of  letters  from 
different  correspondents — all  to  the  effect  that  the  notion  of  new  moon 
on  Saturday  bringing  wet  weather  is  one  of  widely  extended  currency. 
One  correspondent  (who  gives  his  name)  states  that  he  has  constantly 
heard  it  at  sea,  and  among  the  farmers  and  peasantry  in  Scotland, 
Ireland,  and  the  North  of  England.  He  proceeds  thus  :  "  Since  1826, 
nineteen  years  of  the  time  I  have  spent  in  a  seafaring  life.  I  have 
constantly  observed,  though  unable  to  account  for,  the  phenomenon. 
I  have  also  heard  the  stormy  qualities  of  a  Saturday's  moon  remarked 
by  American,  French,  and  Spanish  seamen  ;  and,  still  more  distant, 
a  Chinese  pilot,  who  was  once  doing  duty  on  board  my  vessel  seemed 
to  be  perfectly  cognizant  of  the  fact."  So  that  it  seems  we  have,  in 
giving  currency  to  what  we  only  knew  as  a  very  curious  communica- 
tion from  an  earnest  meteorologist,  been  repeating  what  is  common 
enough  among  sailors  and  farmers.  Another  correspondent  affirms 
that  the  thing  is  most  devoutly  believed  in  by  seamen  ;  who  would  as 
soon  sail  on  a  Friday  as  be  in  the  Channel  after  a  Saturday  moon. — 
After  a  tolerable  course  of  dry  weather,  there  was  some  snow,  accom- 
panied by  wind  on  Saturday  last,  here  in  London  ;  there  were  also 
heavy  louring  clouds.  Sunday  was  cloudy  and  cold,  with  a  little  rain  ; 
Monday  was  louring ;  Tuesday  unsettled ;  Wednesday  quite  over- 
clouded, with  rain  in  the  morning.  The  present  occasion  shows  only 
a  general  change  of  weather,  with  a  tendency  towards  rain.  If  Dr. 
Forster's  theory  be  true,  it  is  decidedly  one  of  the  minor  instances, 
as  far  as  London  weather  is  concerned. — It  will  take  a  good  deal  of 
evidence  to  make  us  believe  in  the  omen  of  a  Saturday  Moon.  But, 
as  we  have  said  of  the  Poughkeepsie  Seer,  the  thing  is  very  curious 
whether  true  or  false.  Whence  comes  this  universal  proverb — and  a 
hundred  others — while  the  meteorological  observer  cannot,  when  he 
puts  down  a  long  series  of  results,  detect  any  weather  cycles  at  all  ? 
One  of  our  correspondents  wrote  us  something  of  a  lecture  for  en- 
couraging, he  said,  the  notion  that  names  could  influence  the  weather. 
He  mistakes  the  question.  If  there  be  any  weather  cycles  depending 
on  the  moon,  it  is  possible  that  one  of  them  may  be  so  related  to  the 
k  cycle  of  seven  days,  as  to  show  recurrences  which  are  of  the  kind 

o  2 


196  A  BUDGET  OF  PARADOXES. 

stated,  or  any  other.  For  example,  we  know  that  if  the  new  moon  of 
March  fall  on  a  Saturday  iu  this  year,  it  will  most  probably  fall  on 
a  Saturday  nineteen  years  hence.  This  is  not  connected  with  the 
spelling  of  Saturday — but  with  the  connexion  between  the  motions  of 
the  sun  and  moon.  Nothing  but  the  Moon  can  settle  the  question — 
and  we  are  willing  to  wait  on  her  for  further  information.  If  the 
adage  be  true,  then  the  philosopher  has  missed  what  lies  before  his 
eyes ;  if  false,  then  the  world  can  be  led  by  the  nose  in  spite  of  the 
eyes.  Both  these  things  happen  sometimes;  and  we  are  willing  to 
take  whichever  of  the  two  solutions  is  borne  out  by  future  facts.  In 
the  mean  time,  we  announce  the  next  Saturday  Moon  for  the  18th 
of  August.' 

How  many  coincidences  are  required  to  establish  a  law  of 
connexion  ?  It  depends  on  the  way  in  which  the  mind  views  the 
matter  in  question.  Many  of  the  paradoxers  are  quite  set  up  by 
a  very  few  instances.  I  will  now  tell  a  story  about  myself,  and 
then  ask  them  a  question. 

So  far  as  instances  can  prove  a  law,  the  following  is  proved :  no 
failure  has  occurred.  Let  a  clergyman  be  known  to  me,  whether 
by  personal  acquaintance  or  correspondence,  or  by  being  frequently 
brought  before  me  by  those  with  whom  I  am  connected  in  private 
life :  that  clergyman  does  not,  except  in  few  cases,  become  a 
bishop ;  but,  if  he  become  a  bishop,  h<e  is  sure,  first  or  last,  to 
become  an  arch-bishop.  This  has  happened  in  every  case.  As 
follows : — 

1.  My  last  schoolmaster,  a  former  Fellow  of  Oriel,  was  a  very 
intimate   college   friend  of  Eichard    Whately,  a  younger  man. 
Struck  by  his  friend's  talents,  he  used  to  talk  of  him  perpetually, 
and   predict   his  future  eminence.      Before  I  was  sixteen,  and 
before  Whately  had  even  given  his  Barnpton  Lectures,  I  was  very 
familiar  with  his  name,  and  some  of  his  sayings.     I  need  not  say 
that  he  became  Archbishop  of  Dublin. 

2.  When  I  was  a  child,  a  first  cousin  of  John  Bird  Sumner 
married  a  sister  of  my  mother.     I  cannot  remember  the  time 
when  I  first  heard  his  name,  but  it  was  made  very  familiar  to  me. 
In  time  he  became  Bishop  of  Chester,  and  then,  Archbishop  of 
Canterbury.     My  reader  may  say  that  Dr.  C.  R.  Sumner,  Bishop 
of  Winchester,  has  just  as  good  a  claim  :  but  it  is  not  so  :  those 
connected  with  me  had  more  knowledge  of  Dr.  J.  B.   Sumner ; 
and  said  nothing,  or  next  to  nothing,  of  the  other.     Rumour  says 
that  the  Bishop  of  Winchester  has  declined  an  Archbishopric :  if 
so,  my  rule  is  a  rule  of  gradations. 

3.  Thomas  Musgrave,  Fellow   of  Trinity  College,  Cambridge, 
was  Dean  of  the  college  when  I  was  an  undergraduate  :    this 


ACCIDENT,  OR  LAW?  197 

brought  me  into  connexion  with  him,  he  giving  impositions  for 
not  going  to  chapel,  I  writing  them  out  according.  We  had 
also  friendly  intercourse  in  after  life ;  I  forgiving,  he  probably 
forgetting.  Honest  Tom  Musgrave,  as  he  used  to  be  called, 
became  Bishop  of  Hereford,  and  Archbishop  of  York. 

4.  About  the  time  when  I  went  to  Cambridge,  I  heard  a  great 
deal  about  Mr.  C.  T.  Longley,  of  Christchurch,   from  a  cousin 
of  my  own  of  the  same  college,  long  since  deceased,  who  spoke  of 
him  much,  and  most  affectionately.     Dr.  Longley  passed  from 
Durham  to  York,  and  thence  to  Canterbury.    I  cannot  quite  make 
out  the  two  Archbishoprics  ;  I  do  not  remember  any  other  private 
channel  through  which    the    name    came  to    me :    perhaps    Dr. 
Longley,  having  two  strings  to   his  bow,  would  have  been  one 
Archbishop  if  I  had  never  heard  of  him. 

5.  When  Dr.  Win.    Thomson   was   appointed   to    the   see    of 
Gloucester  in  1861,  he  and  I  had  been  correspondents  on  the 
subject  of  logic — on    which    we    had  both    written — for   about 
fourteen  years.     On  his  elevation  I  wrote  to  him,  giving  the  pre- 
ceding instances,  and  informing  him  that  he  would  certainly  be 
an  Archbishop.     The  case  was  a  strong  one,  and  the  law  acted 
rapidly;    for  Dr.  Thomson's  elevation  to  the   see  of  York  took 
place  in  1862. 

Here  are  five  cases ;  and  there  is  no  opposing  instance.  I  have 
searched  the  almanacs  since  1828,  and  can  find  no  instance  of  a 
Bishop  not  finally  Archbishop  of  whom  I  had  known  through 
private  sources,  direct  or  indirect.  Now  what  do  my  paradoxers 
say  ?  Is  this  a  pre-established  harmony,  or  a  chain  of  coinci- 
dences ?  And  how  many  instances  will  it  require  to  establish  a 
law? 

Some  account  of  the  great  astronomical  discoveries  lately  made 
by  Sir  John  Herschel  at  the  Cape  of  Good  Hope.  Second 
Edition.  London,  12mo.  1836. 

This  is  a  curious  hoax,  evidently  written  by  a  person  versed  in 
astronomy  and  clever  at  introducing  probable  circumstances  and 
undesigned  coincidences.  It  first  appeared  in  a  newspaper.  It 
makes  Sir  J.  Herschel  discover  men,  animals,  &c.  in  the  moon,  of 
which  much  detail  is  given.  There  seems  to  have  been  a  French 
edition,  the  original,  and  English  editions  in  America,  whence 
the  work  came  into  Britain :  but  whether  the  French  was  pub- 
lished in  America  or  at  Paris  I  do  not  know.  There  is  no  doubt 
that  it  was  produced  in  the  United  States,  by  M.  Nicollet,  an 
astrenomer,  once  of  Paris,  and  a  fugitive  of  some  kind.  About 


198  A  BUDGET  OF  PARADOXES. 

him  I  have  heard  two  stories.  First,  that  he  fled  to  America 
with  funds  not  his  own,  and  that  this  book  was  a  mere  device  to 
raise  the  wind.  Secondly,  that  he  was  a  protege  of  Laplace,  and 
of  the  Polignac  party,  and  also  an  outspoken  man.  That  after 
the  revolution  he  was  so  obnoxious  to  the  republican  party  that 
he  judged  it  prudent  to  quit  France;  which  he  did  in  debt, 
leaving  money  for  his  creditors,  but  not  enough,  with  M.  Bouvard. 
In  America  he  connected  himself  with  an  assurance  office.  The 
moon-story  was  written,  and  sent  to  France,  chiefly  with  the 
intention  of  entrapping  M.  Arago,  Nic'ollet's  especial  foe,  into  the 
belief  of  it.  And  those  who  narrate  this  version  of  the  story 
wind  up  by  saying  that  M.  Arago  was  entrapped,  and  circulated 
the  wonders  through  Paris,  until  a  letter  from  Nicollet  to  M. 
Bouvard  explained  the  hoax.  I  have  no  personal  knowledge  of 
either  story :  but  as  the  poor  man  had  to  endure  the  first,  it  is 
but  right  that  the  second  should  be  told  with  it. 

The  Weather  Almanac  for  the  Year  1838.     By  P.  Murphy,  Esq. 
M.N.S. 

By  M.N.S.  is  meant  member  of  no  society.  This  almanac  bears 
on  the  title-page  two  recommendations.  The  Morning  Post  calls 
it  one  of  the  most  important-if-true  publications  of  our  gene- 
ration. The  Times  says  :  *  If  the  basis  of  his  theory  prove  sound, 
and  its  principles  be  sanctioned  by  a  more  extended  experience, 
it  is  not  too  much  to  say  that  the  importance  of  the  discovery 
is  equal  to  that  of  the  longitude.'  Cautious  journalist !  Three 
times  that  of  the  longitude  would  have  been  too  little  to  .say. 
That  the  landsman  might  predict  the  weather  of  all  the  year,  at 
its  beginning,  Jack  would  cheerfully  give  up  astronomical  longi- 
tude— the  problem — altogether,  and  fall  back  on  chronometers 
with  the  older  Ls,  lead,  latitude,  and  look-out,  applied  to  dead- 
reckoning.  Mr.  Murphy  attempted  to  give  the  weather  day  by 
day :  thus  the  first  seven  days  of  March  bore  Changeable  ;  Eain  ; 
Kain  ;  Rain-wind ;  Changeable  ;  Fair  ;  Changeable.  To  aim  at 
such  precision  as  to  put  a  fair  day  between  two  changeable  ones 
by  weather  theory  was  going  very  near  the  wind  and  weather  too. 
Murphy  opened  the  year  with  cold  and  frost ;  and  the  weather 
did  the  same.  But  Murphy,  opposite  to  Saturday,  January  20, 
put  down  *  Fair,  Probable  lowest  degree  of  winter  temperature.' 
When  this  Saturday  came,  it  was  not  merely  the  probably  cold- 
est of  1838,  but  certainly  the  coldest  of  many  consecutive  years. 
Without  knowing  anything  of  Murphy,  I  felt  it  prudent  to  cover 
my  nose  with  my  glove  as  I  walked  the  street  at  eight  in  the 


MATHEMATICAL   THEOLOGY.  199 

morning.  The  fortune  of  the  Almanac  was  made.  Nobody 
waited  to  see  whether  the  future  would  dement  the  prophecy : 
the  shop  was  beset  in  a  manner  which  brought  the  police  to  keep 
order;  and  it  was  said  that  the  Almanac  for  1838  was  a  gain  of 
5,0001.  to  the  owners.  It  very  soon  appeared  that  this  was  only 
a  lucky  hit :  the  weather-prophet  had  a  modified  reputation  for  a 
few  years ;  and  is  now  no  more  heard  of.  A  work  of  his  will 
presently  appear  in  the  list. 

Letter  from  Alexandria  on  the  evidence  of  the  practical  appli- 
cation of  the  quadrature  of  the  circle  in  the  great  pyramids  of 
Gizeh.  By  H.  C.  Agnew,  Esq.  London,  1838,  4to. 

Mr.  Agnew  detects  proportions  which  he  thinks  were  suggested 
by  those  of  the  circumference  and  diameter  of  a  circle. 

The  creed  of  St.  Athanasius  proved  by  a  mathematical  parallel. 
Before  you  censure,  condemn,  or  approve  ;  read,  examine,  and- 
understand.  E.  B.  REVILO.  London,  1839,  8vo. 

This  author  really  believed  himself,  and  was  in  earnest.  He  is 
not  the  only  person  who  has  written  nonsense  by  confounding  the 
mathematical  infinite  (of  quantity)  with  what  speculators  now 
more  correctly  express  by  the  unlimited,  the  unconditioned,  or 
the  absolute.  This  tract  is  worth  preserving,  as  the  extreme  case 
of  a  particular  kind.  The  following  is  a  specimen.  Infinity 
being  represented  by  oo  ,  as  usual,  and/,  s,  g,  being  finite  integers, 
the  three  Persons  are  denoted  by  oo ',  (m  oo  )',  oo ",  the  finite 
fraction  m  representing  human  nature,  as  opposed  to  oo  .  The 
clauses  of  the  Creed  are  then  given  with  their  mathematical 
parallels.  I  extract  a  couple : — 

But  the  Godhead  of  the  Father,  It  has  been  shown  that  oo-^,  oo', 
of  the  Son,  and  of  the  Holy  Ghost,  and  (m  oo  )  *,  together,  are  but  oo  , 
is  all  one  :  the  glory  equal,  the  and  that  each  is  oo  ,  and  any  magni- 
Majesty  co-eternal.  tude  in  existence  represented  by  oo 

always  was  and  always  will  be :  for 
it  cannot  be  made,  or  destroyed,  and 
yet  exists. 

Equal  to  the  Father,  as  touching  (in  oo  )*  is  equal  to  oo^as  toucli- 
his  Godhead:  and  inferior  to  the  ing  oo  ,  but  inferior  to  oo-^as  touch- 
Father,  as  touching  his  Manhood,  ing  m  :  because  m  is  not  infinite. 

I  might  have  passed  this  over,  as  beneath  even  my  present 
subject,  but  for  the  way  in  which  I  became  acquainted  with  it. 
A  bookseller,  not  the  publisher,  handed  it  to  me  over  his  counter: 
one  who  had  published  mathematical  works.  He  said,  with  an 


200  A   BUDGET   01?'   PARADOXES. 

air  of  important  communication.  Have  you  seen  this,  Sir !    In 

reply,  I  recommended  him  to  show  it  to  my  friend  Mr. ,  for 

whom  he  had  published  mathematics.  Educated  men,  used  to 
books,  and  to  the  converse  of  learned  men,  look  with  mysterious 
wonder  on  such  productions  as  this:  for  which  reason  I  have 
made  a  quotation  which  many  will  judge  had  better  have  been 
omitted.  But  it  would  have  been  an  imposition  on  the  public  if 
I  were,  omitting  this  and  some  other  uses  of  the  Bible  and 
Common  Prayer,  to  pretend  that  I  had  given  a  true  picture  of 
my  school. 

[Since  the  publication  of  the  above,  it  has  been  stated  that  the 
author  is  Mr.  Oliver  Byrne,  the  author  of  the  Dual  Arithmetic 
mentioned  further  on :  E.  B.  Revilo  seems  to  be  obviously  a 
reversal.] 

Old  and  new  logic  contrasted  :  being  an  attempt  to  elucidate,  for 
ordinary  comprehension,  how  Lord  Bacon  delivered  the  human 
mind  from  its  2,000  years'  enslavement  under  Aristotle.  By 
Justin  Brenan.  London,  1839,  12mo. 

Logic,  though  the  other  exact  science,  has  not  had  the  sort  of 
assailants  who  have  clustered  about  Mathematics.  There  is  a 
sect  which  disputes  the  utility  of  logic,  but  there  are  no  special 
points,  like  the  quadrature  of  the  circle,  which  excite  dispute 
among  those  who  admit  other  things.  The  old  story  about 
Aristotle  having  one  logic  to  trammel  us,  and  Bacon  another  to 
set  us  free, — always  laughed  at  by  those  who  really  knew  either 
Aristotle  or  Bacon, — now  begins  to  be  understood  by  a  large 
section  of  the  educated  world.  The  author  of  this  tract  connects 
the  old  logic  with  the  indecencies  of  the  classical  writers,  and  the 
new  with  moral  purity :  he  appeals  to  women,  who,  '  when  they 
see  plainly  the  demoralizing  tendency  of  syllogistic  logic,  they 
will,  no  doubt,  exert  their  powerful  influence  against  it,  and 
support  the  Baconian  method.'  This  is  the  only  work  against 
logic  which  I  can  introduce,  but  it  is  a  rare  one,  I  mean  in 
contents.  I  quote  the  author's  idea  of  a  syllogism  : — 

The  basis  of  this  system  is  the  syllogism.  This  is  a  form  of  couch- 
ing the  substance  of  your  argument  or  investigation  into  one  short 
line  or  sentence — then  corroborating  or  supporting  it  in  another,  and 
drawing  your  conclusion  or  proof  in  a  third. 

On  this  definition  he  gives  an  example,  as  follows :  '  Every  sin 
deserves  death,'  the  substance  of  the  '  argument  or  investigation.' 
Then  comes,  '  Every  unlawful  wish  is  a  sin,'  which  '  corroborates 
or  supports  '  the  preceding  :  and,  lastly,  '  therefore  every  unlaw- 


LOGIC;   SIR  WILLIAM   HAMILTON.  201 

ful  wish  deserves  death,'  which  is  the  '  conclusion  or  proof.'  We 
learn,  also,  that  *  sometimes  the  first  is  called  the  premises  (sic), 
and  sometimes  the  first  premiss  ; '  as  also  that  l  the  first  is  some- 
times called  the  proposition,  or  subject,  or  affirmative,  and  the 
next  the  predicate,  and  sometimes  the  middle  term.'  To  which 
is  added,  with  a  mark  of  exclamation  at  the  end,  '  but,  in  analyz- 
ing the  syllogism,  there  is  a  middle  term,  and  a  predicate  too,  in 
each  of  the  lines  ! '  It  is  clear  that  Aristotle  never  enslaved  this 
mind. 

I  have  said  that  logic  has  no  paradoxers,  but  I  was  speaking  of 
old  time.  This  science  has  slept  until  our  own  day :  Hamilton 
says  there  has  been  *  no  progress  made  in  the  general  develop- 
ment of  the  syllogism  since  the  time  of  Aristotle  ;  and  in  regard 
to  the  few  partial  improvements,  the  professed  historians  seem 
altogether  ignorant.'  But  in  our  time,  the  paradoxer,  the  oppo- 
nent of  common  opinion,  has  appeared  in  this  field.  I  do  not 
refer  to  Prof.  Boole,  who  is  not  a  paradoxer,  but  a  discoverer : 
his  system  could  neither  oppose  nor  support  common  opinion, 
for  its  grounds  were  not  within  the  conception  of  any  one.  I 
speak  especially  of  two  others,  who  fought  like  cat  and  dog : 
one  was  dogmatical,  the  other  categorical.  The  first  was  Hamil- 
ton himself — Sir  William  Hamilton  of  Edinburgh,  the  meta- 
physician, not  Sir  William  Rowan  Hamilton  of  Dublin,  the 
mathematician,  a  combination  of  peculiar  genius  with  unprece- 
dented learning,  erudite  in  all  he  could  want  except  mathematics, 
for  which  he  had  no  turn,  and  in  which  he  had  not  even  a  school- 
boy's knowledge,  thanks  to  the  Oxford  of  his  younger  day.  The 
other  was  the  author  of  this  work,  so  fully  described  in  Hamil- 
ton's writings  that  there  is  no  occasion  to  describe  him  here.  I 
shall  try  to  say  a  few  words  in  common  language  about  the  para- 
doxers. 

Hamilton's  great  paradox  was  the  quantification  of  the  predi- 
cate ;  a  fearful  phrase,  easily  explained.  We  all  know  that  when 
we  say  '  Men  are  animals,'  a  form  wholly  unqualified  in  phrase, 
we  speak  of  all  men,  but  not  of  all  animals :  it  is  some  or  all, 
some  may  be  all  for  aught  the  proposition  says.  This  some-may- 
be-all-for-aught-we-say,  or  not-none,  is  the  logician's  some.  One 
would  suppose  that  '  all  men  are  some  animals,'  would  have  been 
the  logical  phrase  in  all  time :  but  the  predicate  never  was 
quantified.  The  few  who  alluded  to  the  possibility  of  such  a 
thing  found  reasons  for  not  adopting  it  over  and  above  the  great 
reason,  that  Aristotle  did  not  adopt  it.  For  Aristotle  never  ruled 
in  physics  or  metaphysics  in  the  old  time  with  near  so  much  of 


202  A  BUDGET   OF  PARADOXES. 

absolute  sway  as  he  has  ruled  in  logic  down  to  OUT  own  time. 
The  logicians  knew  that  in  the  proposition  '  all  men  are  animals  ' 
the  x  animal '  is  not  universal,  but  particular :  yet  no  one  dared 
to  say  that  all  men  are  some  animals,  and  to  invent  the  phrase, 
'  some  animals  are  all  men '  until  Hamilton  leaped  the  ditch, 
and  not  only  completed  a  system  of  enunciation,  but  applied  it  to 
syllogism. 

My  own  case  is  as  peculiar  as  his :  I  have  proposed  to  intro- 
duce mathematical  thought  into  logic  to  an  extent  which  makes 
the  old  stagers  cry 

St.  Aristotle  !  what  wild  notions  ! 
Serve  a  ne  exeat  regno  on  him ! 

Hard  upon  twenty  years  ago,  a  friend  and  opponent,  who  stands 
high  in  these  matters,  and  who  is  not  nearly  such  a  sectary  of 
Aristotle  and  establishment  as  most,  wrote  to  me  as  follows : — 
6  It  is  said  that  next  to  the  man  who  forms  the  taste  of  a  nation, 
the  greatest  genius  is  the  man  who  corrupts  it.  I  mean  therefore 
no  disrespect,  but  very  much  the  reverse,  when  I  say  that  I 
have  hitherto  always  considered  you  as  a  great  logical  heresiarch.' 
Coleridge  says  he  thinks  that  it  was  Sir  Joshua  Eeynolds  who 
made  the  remark :  which,  to  copy  a  bull  I  once  heard,  I  cannot 
deny,  because  I  was  not  there  when  he  said  it.  My  friend  did 
-  not  call  me  to  repentance  and  reconciliation  with  the  church  : 
I  think  he  had  a  guess  that  I  was  a  reprobate  sinner.  My 
offences  at  that  time  were  but  small:  I  went  on  spinning  syllo- 
gism systems,  all  alien  from  the  common  logic,  until  I  had  six, 
the  initial  letters  of  which,  put  together,  from  the  names  I  gave 
before  I  saw  what  they  would  make,  bar  all  repentance  by  the 
words 

RUE  NOT ! 

leaving  to  the  followers  of  the  old  school  the  comfortable  option 
of  placing  the  letters  thus : 

TRUE  ?  NO  ! 

It  should  however  be  stated  that  the  question  is  not  about 
absolute  truth  or  falsehood.  No  one  denies  that  anything  I  call 
an  inference  is  an  inference :  they  say  that  my  alterations  are 
extra-logical ;  that  they  are  material,  not  formal ;  and  that  logic 
is  a  formal  science. 

The  distinction  between  material  and  formal  is  easily  made, 
where  the  usual  perversions  are  not  required.  A  form  is  an 
empty  machine,  such  as  '  Every  X  is  Y ; '  it  may  be  supplied 
with  matter,  as  in  '  Every  man  is  animal.'  The  logicians  will 


LOGIC  ;  THE  HAMILTON  CONTROVERSY.  203 

foot  see  that  their  formal  proposition,  '  Every  X  is  Y,'  is  material 
in  three  points,  the  degree  of  assertion,  the  quantity  of  the 
proposition,  and  the  copula.  The  purely  formal  proposition  is 
'  There  is  the  probability  a  that  X  stands  in  the  relation  L  to 
Y.'  The  time  will  come  when  it  will  be  regretted  that  logic 
went  without  paradoxers  for  two  thousand  years :  and  when  much 
that  has  been  said  on  the  distinction  of  form  and  matter  will 
breed  jokes. 

I  give  one  instance  of  one  mood  of  each  of  the  systems,  in  the 
order  of  the  letters  first  written  above. 

Relative. — In  this  system  the  formal  relation  is  taken,  that  is, 
the  copula  may  be  any  whatever.  As  a  material  instance,  in 
which  the  relations  are  those  of  consanguinity  (of  men  under- 
stood), take  the  following:  X  is  the  brother  of  Y ;  X  is  not  the 
uncle  of  Z  ;  therefore,  Z  is  not  the  child  of  Y.  The  discussion  of 
relation,  and  of  the  objections  to  the  extension,  is  in  the  Cam- 
bridge Transactions,  vol.  x,  part  2  ;  a  crabbed  conglomerate. 

Undecided. — In  this  system  one  premise,  and  want  of  power 
over  another,  infer  want  of  power  over  a  conclusion.  As  '  Some 
men  are  not  capable  of  tracing  consequences ;  we  cannot  be  sure 
that  there  are  beings  responsible  for  consequences  who  are  in- 
capable of  tracing  consequences  ;  therefore,  we  cannot  be  sure 
that  all  men  are  responsible  for  the  consequences  of  their  ac- 
tions.' 

Exemplar. — This,  long  after  it  suggested  itself  to  me  as  a 
means  of  correcting  a  defect  in  Hamilton's  system,  I  saw  to  be 
the  very  system  of  Aristotle  himself,  though  his  followers  have 
drifted  into  another.  It  makes  its  subject  and  predicate  ex- 
amples, thus :  Any  one  man  is  an  animal ;  any  one  animal  is  a 
mortal ;  therefore,  any  one  man  is  a  mortal. 

Numerical. — Suppose  100  Ys  to  exist:  then  if  70  Xs  be  Ys, 
and  40  Zs  be  Ys,  it  follows  that  10  Xs  (at  least)  are  Zs.  Hamil- 
ton, whose  mind  could  not  generalize  on  symbols,  saw  that  the 
word  most  would  come  under  this  system,  and  admitted,  as  valid, 
such  a  syllogism  as  '  mpst  Ys  are  Xs  ;  most  Ys  are  Zs ;  therefore, 
some  Xs  are  Zs.' 

Onymatic. — This  is  the  ordinary  system  much  enlarged  in 
prepositional  forms.  It  is  fully  discussed  in  my  Syllabus  of 
Logic. 

Transposed. — In  this  syllogism  the  quantity  in  one  premise  is 
transposed  into  the  other.  As,  some  Xs  are  not  Ys ;  for  every  X 
there  is  a  Y  which  is  Z ;  therefore,  some  Zs  are  not  Xs. 

Sir   William  Hamilton   of  Edinburgh   was   one    of  the  best 


204  A  BUDGET   OP  PAKADOXES. 

friends  and  allies  I  ever  had.  When  I  first  began  to  publish 
speculation  on  this  subject,  he  introduced  me  to  the  logical 
world  as  having  plagiarized  from  him.  This  drew  their  attention  : 
a  mathematician  might  have  written  about  logic  under  forms 
which  had  something  of  mathematical  look  long  enough  before  the 
Aristotelians  would  have  troubled  themselves  with  him :  as  was 
done  by  John  Bernoulli,  James  Bernoulli,  Lambert,  and  Grergonne  ; 
who,  when  our  discussion  began,  were  not  known  even  to  omnile- 
gent  Hamilton.  He  retracted  his  accusation  of  wilful  theft  in 
a  manly  way  when  he  found  it  untenable  ;  but  on  this  point  he 
wavered  a  little,  and  was  convinced  to  the  last  that  I  had  taken 
his  principle  unconsciously.  He  thought  I  had  done  the  same 
with  Ploucquet  and  Lambert.  It  was  his  pet  notion  that  I  did 
not  understand  the  commonest  principles  of  logic,  that  I  did  not 
always  know  the  difference  between  the  middle  term  of  a  syllo- 
gism and  its  conclusion.  It  went  against  his  grain  to  imagine 
that  a  mathematician  could  be  a  logician.  So  long  as  he 
took  me  to  be  riding  my  own  hobby,  he  laughed  consumedly : 
but  when  he  thought  he  could  make  out  that  I  was  mounted 
behind  Ploucquet  or  Lambert,  the  current  ran  thus : — '  It  would 
indeed  have  been  little  short  of  a  miracle  had  he,  ignorant  even 
of  the  common  principles  of  logic,  been  able  of  himself  to  rise  to 
generalization  so  lofty  and  so  accurate  as  are  supposed  in  the 
peculiar  doctrines  of  both  the  rival  logicians,  Lambert  and 
Ploucquet — how  useless  soever  these  may  in  practice  prove  to  be. 
All  this  has  been  sufficiently  discussed  elsewhere  :  '  but,  masters, 
remember  that  I  am  an  ass.' 

I  know  that  I  never  saw  Lambert's  work  until  after  all 
Hamilton  supposed  me  to  have  taken  was  written :  he  himself, 
who  read  almost  everything,  knew  nothing  about  it  until  after  I 
did.  I  cannot  prove  what  I  say  about  my  knowledge  of  Lambert : 
but  the  means  of  doing  it  may  turn  up.  For,  by  the  casual 
turning  up  of  an  old  letter,  I  have  found  the  means  of  clearing 
myself  as  to  Ploucquet.  Hamilton  assumed  that  (unconsciously) 
I  took  from  Ploucquet  the  notion  of  a  logical  notation  in  which 
the  symbol  of  the  conclusion  is  seen  in  the  joint  symbols  of  the 
premises.  For  example,  in  my  own  fashion  I  write  down  (•)(•)' 
two  symbols  of  premises.  By  these  symbols  I  see  that  there  is  a 
valid  conclusion,  and  that  it  may  be  written  in  symbol  by  striking 
out  the  two  middle  parentheses,  which  gives  (  .  .  )  and  reading 
the  two  negative  dots  as  an  affirmative.  And  so  I  see  in  (.)(.) 
that  (  )  is  the  conclusion.  This,  in  full,  is  the  perception  that 
*  all  are  either  Xs  or  Ys '  and  '  all  are  either  Ys  or  Zs '  necessitates 
'gome  Xs  are  Zs.'  Now  in  Ploucquet's  book  of  1763,  is  found, 


CONTROVERSY  WITH  HAMILTON.  205 

1  Deleatur  in  praemissis  medius ;  id  quod  restat  indicat  con- 
clusionem.'  In  the  paper  in  which  I  explain  my  symbols — which 
are  altogether  different  from  Ploucquet's — there  is  found  '  Erase 
the  symbols  of  the  middle  term  ;  the  remaining  symbols  show 
the  inference.'  There  is  very  great  likeness :  and  I  would  have 
excused  Hamilton  for  his  notion  if  he  had  fairly  given  reference  to 
the  part  of  the  book  in  which  his  quotation  was  found.  For  I 
had  shown  in  my  Formal  Logic  what  part  of  Ploucquet's  book  I 
had  used :  and  a  fair  disputant  would  either  have  strengthened 
his  point  by  showing  that  I  had  been  at  his  part  of  the  book,  or 
allowed  me  the  advantage  of  it  being  apparent  that  I  had  not 
given  evidence  of  having  seen  that  part  of  the  book.  My  good 
friend,  though  an  honest  man,  was  sometimes  unwilling  to  allow 
due  advantage  to  controversial  opponents. 

But  to  my  point.  The  only  work  of  Ploucquet  I  ever  saw  was 
lent  me  by  my  friend  Dr.  Logan,  with  whom  I  have  often  corres- 
ponded on  logic,  &c.  I  chanced  (in  1865)  to  turn  up  the  letter 
which  he  sent  me  (Sept.  12,  1847)  with  the  book.  Part  of  it 
runs  thus : — '  I  congratulate  you  on  your  success  in  your  logical 
researches  [that  is,  in. asking  for  the  book,  I  had  described  some 
results].  Since  the  reading  of  your  first  paper  I  have  been 
satisfied  as  to  the  possibility  of  inventing  a  logical  notation  in 
which  the  rationale  of  the  inference  is  contained  in  the  symbol, 
though  I  never  attempted  to  verify  it  [what.  I  communicated, 
then,  satisfied  the  writer  that  I  had  done  and  communicated  what 
he,  from  my  previous  paper,  suspected  to  be  practicable],  I 
send  you  Ploucquet's  dissertation.  .  .  .' 

It  now  being  manifest  that  I  cannot  be  souring  grapes  which 
have  been  taken  from  me,  I  will  say  what  I  never  said  in  print 
before.  There  is  not  the  slightest  merit  in  making  the  symbols 
of  the  premises  yield  that  of  the  conclusion  by  erasure  :  the  thing 
must  do  itself  in  every  system  which  symbolises  quantities.  For 
in  every  syllogism  (except  the  inverted  Bramantip  of  the  Aristo- 
telians) the  conclusion  is  manifest  in  this  way  without  symbols. 
This  Bramantip  destroys  system  in  the  Aristotelian  lot:  and 
circumstances  which  I  have  pointed  out  destroy  it  in  Hamilton's 
own  collection.  But  in  that  enlargement  of  the  reputed  Aristo- 
telian system  which  I  have  called  onymatic,  and  in  that  correction 
of  Hamilton's  system  which  I  have  called  exemplar,  the  rule  of 
erasure  is  universal,  and  may  be  seen  without  symbols. 

Our  first  controversy  was  in  1846.  In  1847,  in  my  Formal 
Logic,  I  gave  him  back  a  little  satire  for  satire,  just  to  show,  as 
1  stated,  that  I  could  employ  ridicule  if  I  pleased.  He  was  so 


206  A  BUDGET  OF  PARADOXES. 

offended  with  the  appendix  in  which  this  was  contained,  that  he 
would  not  accept  the  copy  of  the  book  I  sent  him,  but  returned 
it.  Copies  of  controversial  works,  sent  from  opponent  to  opponent, 
are  not  presents,  in  the  usual  sense :  it  was  a  marked  success  to 
make  him  angry  enough  to  forget  this.  It  had  some  effect  how- 
ever :  during  the  rest  of  his  life  I  wished  to  avoid  provocation  ;  for 
I  could  not  feel  sure  that  excitement  might  not  produce  con- 
sequences. I  allowed  his  slashing  account  of  me  in  the  Discus- 
sions to  pass  unanswered  :  and  before  that,  when  he  proposed  to 
open  a  controversy  in  the  Athenaeum  upon  my  second  Cambridge 
paper,  I  merely  deferred  the  dispute  until  the  next  edition  of  my 
Formal  Logic.  I  cannot  expect  the  account  in  the  Discussions 
to  amuse  an  unconcerned  reader  as  much  as  it  amused  myself : 
but  for  a  cut-and-thrust,  might-and-main,  tooth-and-nail,  ham- 
mer-and-tongs  assault,  I  can  particularly  recommend  it.  I  never 
knew,  until  I  read  it,  how  much  I  should  enjoy  a  thundering 
onslaught  on  myself,  done  with  racy  insolence  by  a  master  hand, 
to  whom  my  good  genius  had  whispered  Ita  feri  ut  se  sentiat 
emori.  Since  that  time  I  have,  as  the  Irishman  said,  become  '  dry 
moulded  for  want  of  a  bating.'  Some  of  my  paradoxers  have 
done  their  best :  but  theirs  is  mere  twopenny — '  small  swipes,'  as 
Peter  Peebles  said.  Brandy  for  heroes !  I  hope  a  reviewer  or  two 
will  have  mercy  on  me,  and  will  give  me  as  good  discipline  as 
Strafford  would  have  given  to  Hampden  and  his  set:  'much 
beholden,'  said  he,  '  should  they  be  to  any  one  that  should 
thoroughly  take  pains  with  them  in  that  kind  ' — meaning  objective 
flagellation.  And  I  shall  be  the  same  to  any  one  who  will  serve 
me  so — but  in  a  literary  and  periodical  sense :  my  corporeal 
cuticle  is  as  thin  as  my  neighbours'. 

Sir  W.  H.  was  suffering  under  local  paralysis  before  our  con- 
troversy commenced  :  and  though  his  mind  was  quite  unaffected, 
a  retort  of  as  downright  a  character  as  the  attack  might  have 
produced  serious  effect  upon  a  person  who  had  shown  himself 
sensible  of  ridicule.  Had  a  second  attack  of  his  disorder  followed 
an  answer  from  me,  I  should  have  been  held  to  have  caused  it : 
though,  looking  at  Hamilton's  genial  love  of  combat,  I  strongly 
suspected  that  a  retort  in  kind 

Would  cheer  his  heart,  and  warm  his  blood, 
And  make  him  fight,  and  do  him  good. 

But  I  could  not  venture  to  risk  it.  So  all  I  did,  in  reply  to  the 
article  in  the  Discussions,  was  to  write  to  him  the  following  note  : 
which,  as  illustrating  an  etiquette  of  controversy,  I  insert. 


LETTER   TO   HAMILTON— DOGGR EL.  207 

'  I  beg  to  acknowledge  and  thank  you  for  .  .  .  It  is  necessary  that  I 
should  say  a  word  on  my  retention  of  this  work,  with  reference  to 
your  return  of  the  copy  of  my  '  Formal  Logic,'  which  I  presented  to 
you  on  its  publication  :  a  return  made  on  the  ground  of  your  disap- 
proval of  the  account  of  our  controversy  which  that  work  contained. 
According  to  my  view  of  the  subject,  any  one  whose  dealing  with  the 
author  of  a  book  is  specially  attacked  in  it,  has  a  right  to  expect  from 
the  author  that  part  of  the  book  in  which  the  attack  is  made,  together 
with  so  much  of  the  remaining  part  as  is  fairly  context.  And  I  hold 
that  the  acceptance  by  the  party  assailed  of  such  work  or  part  of  a  work 
does  not  imply  any  amount  of  approval  of  the  contents,  or  of  want  of 
disapproval.  On  this  principle  (though  I  am  not  prepared  to  add  the 
word  alone)  I  forwarded  to  you  the  whole  of  my  work  on  "  Formal 
Logic  "  and  my  second  Cambridge  Memoir.  And  on  this  principle  I 
should  have  held  you  wanting  in  due  regard  to  my  literary  rights  if 
you  had  not  forwarded  to  me  your  asterisked  pages,  with  all  else  that 
was  necessary  to  a  full  understanding  of  their  scope  and  meaning,  so 
far  as  the  contents  of  the  book  would  furnish  it.  For  the  remaining 
portion,  which  it  would  be  a  hundred  pities  to  separate  from  the  pag^es 
in  which  I  am  directly  concerned,  I  am  your  debtor  on  another  princi- 
ple ;  and  shall  be  glad  to  remain  so  if  you  will  allow  me  to  make  a 
feint  of  balancing  the  account  by  the  offer  of  two  small  works  on  sub- 
jects as  little  connected  with  our  discussion  as  the  "  Epistolae  Obscuro- 
rum  Yirorum,"  or  the  Lutheran  dispute.  I  trust  that  by  accepting 
my  "  Opuscula  "  you  will  enable  me  to  avoid  the  use  of  the  knife,  and 
leave  me  to  cut  you  up  with  the  pen  as  occasion  shall  serve,  I  remain, 
&c.  (April  21,  1852).' 

I  received  polite  thanks,  but  not  a  word  about  the  body  of  the 
letter :  my  argument,  I  suppose,  was  admitted. 

I  find  among  my  miscellaneous  papers  the  following  jeu 
desprit,  or  jeu  de  betise,  whichever  the  reader  pleases — I  care 
not  — intended,  before  I  saw  ground  for  abstaining,  to  have,  as  the 
phrase  is,  come  in  somehow.  I  think  I  could  manage  to  bring 
anything  into  anything :  certainly  into  a  Budget  of  Paradoxes. 
Sir  W.  H.  rather  piqued  himself  upon  some  caniculars,  or  doggrel 
verses,  which  he  had  put  together  in  memoriam  [technicam]  of 
the  way  in'  which  A  E  I  0  are  used  in  logic  :  he  added  U,  Y,  for 
the  addition  of  meet,  &c.  to  the  system.  I  took  the  liberty  of 
concocting  some  counter-doggrel,  just  to  show  that  a  mathema- 
tician may  have  architectonic  power  as  well  as  a  metaphysician. 


208  A  BUDGET   OF  PAEADOXES. 

DOGGREL. 
BY  SIR  W.  HAMILTON. 

A  it  affirms  of  this,  these,  all, 

Whilst  E  deries  of  any  • 
I  it  affirms  (whilst  O  denies) 

Of  some  (or  few,  or  many). 

Thus  A  affirms,  as  E  denies, 

And  definitely  either ; 
Thus  I  affirms,  as  0  denies, 

And  definitely  neither. 

A  half,  left  semidefinite, 

Is  worthy  of  its  score  ; 
TJ,  then,  affirms,  as  Y  denies, 

This,  neither  less  nor  more. 

Indefinito-definites, 

I,  UI,  YO,  last  we  come ; 
And  this  affirms,  as  that  denies 

Of  more,  most  (half,  plus,  some). 

COUNTER  DOGGREL. 

BY  PROF.  DE  MORGAN. 
(1847.) 

GREAT  A  affirms  of  all ; 

SJr  William  does  so  too  : 
When  the  subject  is  '  my  suspicion,' 

And  the  predicate  '  must  be  true.' 

Great  E  denies  of  all ; 

Sir  William  of  all  but  one  : 
When  he  speaks  about  this  present  time, 

And  of  those  who  in  logic  have  done. 

Great  I  takes  up  but  some  ; 

Sir  William  !  my  dear  soul ! 
Why  then  in  all  your  writings, 

Does  '  Great  I '  fill1  the  whole  ! 

1  A  very  truculently  unjust  assertion  :  for  Sir  W.  was  as  great  a  setter  up  of  some 
as  lie  was  a  puller  down  of  others.  His  writings  are  a  congeries  of  praises  and 
blames,  both  cruel  smart,  as  they  say  in  the  States.  But  the  combined  instigation  of 


LOGICAL  DOGGREL.  209 

Great  O  says  some  are  not ; 

Sir  William's  readers  catch, 
That  some  (modern)  Athens  is  not  without 

An  Aristotle  to  match, 

*  A  half,  left  semi-definite, 

Is  worthy  of  its  score : ' 
This  looked  very  much  like  balderdash, 

And  neither  less  nor  more. 

It  puzzled  me  like  anything  ; 

In  fact,  it  puzzled  me  worse  : 
Isn't  schoolman's  logic  hard  enough, 

Without  being  in  Sibyl's  verse  ? 

At  last,  thinks  I,  'tis  German  ; 

And  I'll  try  it  with  some  beer ! 
The  landlord  asked  what  bothered  me  so, 

And  at  once  he  made  it  clear. 

It's  half-and-half,  the  gentleman  means ; 

Don't  you  see  he  talks  of  score  ? 
That's  the  bit  of  a  memorandum 

That  we  chalk  behind  .the  door. 

Semi-definite  's  outlandish ; 

But  I  see,  in.  half  a  squint, 
That  he  speaks  of  the  lubbers  who  call  for  a  quart, 

When  they  can't  manage  more  than  a  pint. 

Now  I'll  read  it  into  English, 

And  then  you'll  answer  me  this  : 
If  it  isn't  good  logic  all  the  world  round, 

I  should  like  to  know  what  is  ? 

When  you  call  for  a  pot  of  half-and-half, 

If  you're  lost  to  sense  of  shame, 
You  may  leave  it  semi-definite, 

But  you  pay  for  it  all  just  the  same. 


I  am  unspeakably  comforted  when  I  look  over  the  above  in 
remembering  that  the  question  is  not  whether  it  be  Pindaric  or 

prose,  rhyme,  and  retort  would  send  Aristides  himself  to  Tartarus,  if  it  were  not 
pretty  certain  that  Minos  would  grant  a  stet  proccssits  under  the  circumstances.  The 
first  two  verses  are  exaggerations  standing  on  a  basis  of  truth.  The  fourth  verse  is 
quite  true :  Sir  W.  H.  was  an  Edinburgh  Aristotle,  with  the  differences  of  ancient  and 
modern  Athens  well  marked,  especially  the  perfervidum  inginium  Scot&rum. 

P 


210  A   BUDGET  OF  PARADOXES. 

Horatian,  but  whether  the  copy  be  as  good  as  the  original.  And 
I  say  it  is  :  and  will  take  no  denial. 

Long  live — long  will  live — the  glad  memory  of  William 
Hamilton,  Good,  Learned,  Acute,  and  Disputatious !  He  fought 
upon  principle  :  the  motto  of  his  book  is — 

Truth,  like  a  torch,  the  more  it's  shook  it  shines. 

There  is  something  in  this ;  but  metaphors,  like  puddings, 
quarrels,  rivers,  and  arguments,  always  have  two  sides  to  them. 
For  instance, 

Truth,  like  a  torch,  the  more  ifc  's  shook  it  shines ; 

But  those  who  want  to  use  it,  hold  it  steady. 
They  shake  the  flame  who  like  a  glare  to  gaze  at, 

They  keep  it  still  who  want  a  light  to  see  by. 


Theory  of  Parallels.  The  proof  of  Euclid's  axiom  looked  for  in 
the  properties  of  the  Equiangular  Spiral.  By  Lieut-Col.  G.  Per- 
ronet  Thompson.  The  same,  second  edition,  revised  and  cor- 
rected. The  same,  third  edition,  shortened,  and  freed  from 
dependence  on  the  theory  of  limits.  The  same,  fourth  edition, 
ditto,  ditto.  All  London,  1840,  8vo. 

To  explain  these  editions  it  should  be  noted  that  General 
Thompson  rapidly  modified  his  notions,  and  republished  his  tracts 
accordingly. 

Vestiges  of  the  Natural  History  of  Creation.     London,  1840, 12mo. 

This  is  the  first  edition  of  this  celebrated  work.  Its  form  is  a 
case  of  the  theory :  the  book  is  an  undeniable  duodecimo,  but  the 
size  of  its  paper  gives  it  the  look  of  not  the  smallest  of  octavos. 
Does  not  this  illustrate  the  law  of  development,  the  gradation  of 
families,  the  transference  of  species,  and  so  on  ?  If  so,  I  claim 
the  discovery  of  this  esoteric  testimony  of  the  book  to  its  own 
contents ;  I  defy  any  one  to  point  out  the  reviewer  who  has 
mentioned  it.  The  work  itself  is  described  by  its  author  aa  '  the 
first  attempt  to  connect  the  natural  sciences  into  a  history  of 
creation.'  The  attempt  was  commenced,  and  has  been  carried 
on,  both  with  marked  talent,  and  will  be  continued.  Great 
advantage  will  result :  at  the  worst  we  are  but  in  the  alchemy  of 
some  new  chemistry,  or  the  astrology  of  some  new  astronomy. 
Perhaps  it  would  be  as  well  not  to  be  too  sure  on  the  matter, 
until  we  have  an  antidote  to  possible  consequences  as  ex- 


THE  VESTIGES   OF  CREATION.  211 

hibited  under  another  theory,  on  which  it  is  as  reasonable  to 
speculate  as  on  that  of  the  '  Vestiges.'  I  met  long  ago  with  a 
splendid  player  on  the  guitar,  who  assured  me,  and  was  confirmed 
by  his  friends,  that  he  never  practised,  except  in  thought,  and 
did  not  possess  an  instrument :  he  kept  his  fingers  acting  in  his 
mind,  until  they  got  their  habits ;  and  thus  he  learnt  the  most 
difficult  novelties  of  execution.  Now  what  if  this  should  be  a 
minor  segment  of  a  higher  law  ?  What  if,  by  constantly  think- 
ing of  ourselves  as  descended  from  primaeval  monkeys,  we  should, 
— if  this  be  true — actually  get  our  tails  again?  What  if  the 
first  man  who  was  detected  with  such  an  appendage  should  be 
obliged  to  confess  himself  the  author  of  the  '  Vestiges  ' — a  person 
yet  unknown — who  would  naturally  get  the  start  of  his  species 
by  having  had  the  earliest  habit  of  thinking  on  the  mattei  ?  I 
confess  I  never  hear  a  man  of  note  talk  fluently  about  it  without  a 
curious  glance  at  his  proportions,  to  see  whether  there  may  be 
ground  to  conjecture  that  he  may  have  more  of  '  mortal  coil ' 
than  others,  in  anaxyridical  concealment.  I  do  not  feel  sure 
that  even  a  paternal  love  for  his  theory  would  induce  him,  in  the 
case  I  am  supposing,  to  exhibit  himself  at  the  British  Associa- 
tion, 

With  a  hole  behind  which  his  tail  peeped  through. 

The  first  sentence  of  this  book  (1840)  is  a  cast  of  the  log,  which 
shows  our  rate  of  progress.  '  It  is  familiar  knowledge  that  the 
earth  which  we  inhabit  is  a  globe  of  somewhat  less  than  8,000 
miles  in  diameter,  being  one  of  a  series  of  eleven  which  revolve  at 
different  distances  around  the  sun.'  The  eleven !  Not  to  mention 
the  Iscariot  which  Le  Verrier  and  Adams  calculated  into  existence, 
there  is  more  than  a  septuagint  of  new  planetoids. 

The  Constitution  and  Rules  of  the  Ancient  and  Universal  '  Benefit 
Society '  established  by  Jesus  Christ,  exhibited,  and  its  advan- 
tages and  claims  maintained,  against  all  Modern  and  merely 
Human  Institutions  of  the  kind  :  A  Letter  very  respectfully  ad- 
dressed to  the  Rev.  James  Everett,  and  occasioned  by  certain 
remarks  made  by  him,  in  a  speech  to  the  Members  of  the 
*  Wesleyan  Centenary  Institute '  Benefit  Society.  Dated  York, 
Dec.  7,  1840.  By  Thomas  Smith.  12mo.  (pp.  8.) 

The  Wesleyan  minister  addressed  had  advocated  provision 
against  old  age,  &c. :  the  writer  declares  all  private  provision 
unchristian.  After  decent  maintenance  and  relief  of  family 
claims  of  indigence,  he  holds  that  all  the  rest  is  to  go  to  the 
'  Benefit  Society,'  of  which  he  draws  up  the  rules,  in  technical 

F   2 


212  A  BUDGET   OF  PARADOXES. 

form,  with  chapters  of  '  Officers,'  *  Contributors,'  &c.,  from  the 
Acts  of  the  Apostles,  &c.,  and  some  of  the  early  Fathers.  He 
holds  that  a  Christian  may  not  '  make  a  private  provision  against 
the  contingencies  of  the  future : '  and  that  the  great  '  Benefit 
Society '  is  the  divinely-ordained  recipient  of  all  the  surplus  of 
his  income ;  capital,  beyond  what  is  necessary  for  business,  he 
is  to  have  none.  A  real  good  speculator  shuts  his  eyes  by 
instinct,  when  opening  them  would  not  serve  the  purpose:  he 
has  the  vizor  of  the  Irish  fairy  tale,  which  fell  of  itself  over  the 
eyes  of  the  wearer  the  moment  he  turned  them  upon  the  en- 
chanted light  which  would  have  destroyed  him  if  he  had  caught 
sight  of  it.  'Whiles  it  remained,  was  it  not  thine  own?  and 
after  it  was  sold,  was  it  (the  purchase-money)  not  in  thine  own 
power?'  would  have  been  awkward  to  quote,  and  accordingly 
nothing  is  stated  except  the  well-known  result,  which  is  rule  3, 
cap.  5,  '  Prevention  of  Abuses.'  By  putting  his  principles  to- 
gether, the  author  can  be  made,  logically,  to  mean  that  the 
successors  of  the  apostles  should  put  to  death  all  contributors  who 
are  detected  in  not  paying  their  full  premiums. 

I  have  known  one  or  two  cases  in  which  policy-holders  have 
surrendered  their  policies  through  having  arrived  at  a  conviction 
that  direct  provision  is  unlawful.  So  far  as  I  could  make  it  out, 
these  parties  did  not  think  it  unlawful  to  lay  by  out  of  income, 
except  when  this  was  done  in  a  manner  which  involved  calcula- 
tion of  death-chances.  It  is  singular  they  did  not  see  that  the 
entrance  of  chance  of  death  was  the  entrance  of  the  very  principle 
of  the  benefit  society  described  in  the  Acts  of  the  Apostles.  The 
family  of  the  one  who  died  young  received  more  in  proportion  to 
premiums  paid  than  the  family  of  the  one  who  died  old.  Every 
one  who  understands  life  assurance  sees  that — bonus  apart — the 
difference  between  an  assurance  office  and  a  savings  bank  consists 
in  the  adoption,  pro  tanto,  of  the  principle  of  community  of 
goods.  In  the  original  constitution  of  the  oldest  assurance  office, 
the  Amicable  Society,  the  plan  with  which  they  started  was 
nothing  but  this :  persons  of  all  ages  under  forty-five  paid  one 
common  premium,  and  the  proceeds  were  divided  among  the 
representatives  of  those  who  died  within  the  year. 

[I  omitted  from  its  proper  place  a  manuscript  quadrature 
(3' 14 16  exactly)  addressed  to  an  eminent  mathematician,  dated 
in  1842  from  the  debtors'  ward  of  a  country  gaol.  The  unfortu- 
nate speculator  says,  '  I  have  laboured  many  years  to  find  the 
precise  ratio.'  I  have  heard  of  several  cases  in  which  squaring 


PEEPETUAL   MOTION — GEAVITATION   AND   MAGNETISM.      £13 

the  circle  has  produced  an  inability  to  square  accounts.  I  re- 
mind those  who  feel  a  kind  of  inspiration  to  employ  native 
genius  upon  difficulties,  without  gradual  progression  from  ele- 
ments, that  the  call  is  one  which  becomes  stronger  and  stronger, 
and  may  lead,  as  it  has  led,  to  abandonment  of  the  duties  of  life, 
and  all  the  consequences.] 

1842.  Provisional  Prospectus  of  the  Double  Acting  Rotary  Engine 
Company.  Also  Mechanic's  Magazine,  March  26,  1842. 

Perpetual  motion  by  a  drum  with  one  vertical  half  in  mercury, 
the  other  in  a  vacuum :  the  drum,  I  suppose,  working  round  for 
ever  to  find  an  easy  position.  Steam  to  be  superseded :  steam 
and  electricity  convulsions  of  nature  never  intended  by  Provi- 
dence for  the  use  of  man.  The  price  of  the  present  engines, 
as  old  iron,  will  buy  new  engines  that  will  work  without  fuel 
and  at  no  expense.  Guaranteed  by  the  Count  de  Predaval,  the 
discoverer.  I  was  to  have  been  a  Director,  but  my  name  got  no 
further  than  ink,  and  not  so  far  as  official  notification  of  the 
honour,  partly  owing  to  my  having  communicated  to  the 
Mechanic's  Magazine  information  privately  given  to  me,  which 
gave  premature  publicity,  and  knocked  up  the  plan. 

An  Exposition  of  the  Nature,  Force,  Action,  and  other  properties 
of  Gravitation  on  the  Planets.  London,  1842,  12mo. 

An  Investigation  of  the  principles  of  the  Rules  for  determining  the 
Measures  of  the  Areas  and  Circumferences  of  Circular  Plane 
Surfaces  .  .  .  London,  1844,  8vo. 

These  are  anonymous ;  but  the  author  (whom  I  believe  to  be 
Mr.  Denison,  presently  noted)  is  described  as  author  of  a  new 
system  of  mathematics,  and  also  of  mechanics.  He  had  need 
have  both,  for  he  shows  that  the  line  which  has  a  square  equal 
to  a  given  circle,  has  a  cube  equal  to  the  sphere  on  the  same 
diameter :  that  is,  in  old  mathematics,  the  diameter  is  to  the 
circumference  as  9  to  161  Again,  admitting  that  the  velocities 
of  planets  in  circular  orbits  are  inversely  as  the  square  roots  of 
their  distances,  that  is,  admitting  Kepler's  law,  he  manages  to 
prove  that  gravitation  is  inversely  as  the  square  root  of  the 
distance :  and  suspects  magnetism  of  doing  the  difference  be- 
tween this  and  Newton's  law.  Magnetism  and  electricity  are,  in 
physics,  the  member  of  parliament  and  the  cabman — at  every 
man's  bidding,  as  Henry  Warburton  said. 


214  A  BUDGET   OF  PARADOXES. 

The  above  is  an  outrageous  quadrature.  In  the  preceding  year, 
1841,  was  published  what  I  suppose  at  first  to  be  a  Maori  quadra- 
ture, by  Maccook.  But  I  get  it  from  a  cutting  out  of  some 
French  periodical,  and  I  incline  to  think  that  it  must  be  by  a 
Mr.  M'Cook.  He  maks  TT  to  be  2  +  2  V(8  V  2  - 1 1). 


Refutation  of  a  Pamphlet  written  by  the  Rev.  John  Mackey, 
R.C.P.,  entitled  '  A  method  of  making  a  cube  double  of  a  cube, 
founded  on  the  principles  of  elementary  geometry,'  wherein  his 
principles  are  proved  erroneous,  and  the  required  solution  not 
yet  obtained.  By  Robert  Murphy.  Mallow,  1824,  12mo. 

This  refutation  was  the  production  of  an  Irish  boy  of  eighteen 
years  old,  self-educated  in  mathematics,  the  son  of  a  shoemaker 
at  Mallow.  He  died  in  1843,  leaving  a  name  which  is  well 
known  among  mathematicians.  His  works  on  the  theory  of 
equations  and  on  electricity,  and  his  papers  in  the  Cambridge 
Transactions,  are  all  of  high  genius.  The  only  account  of  him 
which  I  know  of  is  that  which  I  wrote  for  the  Supplement  of  the 
Penny  Cyclopaedia.  He  was  thrown  by  his  talents  into  a  good 
income  at  Cambridge,  with  no  social  training  except  penury,  and 
very  little  intellectual  training  except  mathematics.  He  fell 
into  dissipation,  and  his  scientific  career  was  almost  arrested  : 
but  he  had  great  good  in  him,  to  my  knowledge.  A  sentence  in 
a  letter  from  the  late  Bean  Peacock  to  me — giving  some  advice 
about  the  means  of  serving  Murphy — sets  out  the  old  case : 
*  Murphy  is  a  man  whose  special  education  is  in  advance  of  his 
general',  and  such  men  are  almost  always  difficult  subjects  to 
manage.'  This  article  having  been  omitted  in  its  proper  place, 
I  put  it  at  1843,  the  date  of  Murphy's  death. 


The  Invisible  Universe  disclosed ;  or,  the  real  Plan  and  Govern- 
ment of  the  Universe.  By  Henry  Coleman  Johnson,  Esq. 
London,  1843,  8vo. 

The  book  opens  abruptly  with — 

"  First  demonstration.  Concerning  the  centre :  showing  that,  be- 
cause the  centre  is  an  innermost  point  at  an  equal  distance  between 
two  extreme  points  of  a  right  line,  and  from  every  two  relative  and 
opposite  intermediate  points,  it  is  composed  of  the  two  extreme  in- 
ternal points  of  each  half  of  the  line ;  each  extreme  internal  point 
attracting  towards  itself  all  parts  of  that  half  to  which  it  belongs  .  .  ." 


THE   COMET   OF    1843.  215 

Of  course  the  circle  is  squared:  and  the  circumference  is  3^ 
diameters. 

Combination  of  the  Zodiacal  and  Cometical  Systems.     Printed  for 
the  London  Society,  Exeter  Hall.     Price  Sixpence,   (n.d.  1843.) 

What  this  London  Society  was,  or  the  '  combination,'  did  not 
appear.  There  was  a  remarkable  comet  in  1843,  the  tail  of 
which  was  at  first  confounded  with  what  is  called  the  zodiacal 
light.  This  nicely-printed  little  tract,  evidently  got  up  with 
less  care  for  expense  than  is  usual  in  such  works,  brings  together 
all  the  announcements  of  the  astronomers,  and  adds  a  short  head 
and  tail  piece,  which  I  shall  quote  entire.  As  the  announce- 
ments are  very  ordinary  astronomy,  the  reader  will  be  able  to 
detect,  if  detection  be  possible,  what  is  the  meaning  and 
force  of  the  '  Combination  of  the  Zodiacal  and  Cometical  Sys- 
tems ' : — 

"  Premonition.  It  h^s  pleased  the  AUTHOR  OF  CREATION  to  cause  (to 
His  human  and  reasoning  Creatures  of  this  generation,  by  a  '  combined ' 
appearance  in  His  Zodiacal  and  Cometical  systems)  a  '  warning  Crisis  ' 
of  universal  concernment  to  this  our  GLOBE.  It  is  this  '  Crisis '  that 
has  so  generally  '  ROUSED  '  at  this  moment  the  '  nations  throughout  the 
Earth '  that  no  equal  interest  has  ever  before  been  excited  by  MAN  ; 
unless  it  be  in  that  caused  by  the  '  PAGAN- TEMPLE  IN  ROME,' which 
is  recorded  by  the  elder  Pliny,  l  Nat.  Hist.'  i.  23.  iii.  3.  HARDOUIN." 

After  the  accounts  given  by  the  unperceiving  astronomers,  comes 
what  follows : — 

"  Such  has  been  (hitherto)  the  only  object  discerned  by  the  '  Wise  of 
this  World,'  in  this  twofold  union  of  the  '  Zodiacal '  and  '  Cometical ' 
systems :  yet  it  is  nevertheless  a  mcst  '  Thrilling  Warning,'  to  all  the 
inhabitants  of  this  precarious  and  transitory  EARTH.  We  have  no 
authorized  intimation,  or  reasonable  prospective  contemplation,  of 

*  current  time  '  beyond  a  year  1860,  of  the  present  century  ;  or  rather, 
except  '  the  interval  which  may  now  remain  from  the  present  year  3843, 
to  a  year  I860'  (»/ju£pac  E2CHKONTA — 'threescore  or  sixty  days  ' — 'I 
have  appointed  each  "  DAT  "  for  a  "  YEAR,"  '    Ezek.  iv.  6)  :  and  we  know, 
from  our  '  common  experience,'  how  speedily  such  a  measure  of  time 
will  pass  away. 

No  words  can  be  '  more  explicit '  than  these  of  OUR  BLESSED  LORD  : 
viz.  '  THIS  GOSPEL  of  the  Kingdom  shall  be  preached  in  ALL  the  EARTH, 
for  a  Witness  to  ALL  NATIONS  ;  AND  THEN,  shall  the  END  COME.'  The 

*  next   18   years '    must   therefore  supply  the  interval  of  the  '  special 
Episcopal  forerunners.' 

(Matt.  xxiv.  14.) 
See  the    '  JEWISH    INTELLIGENCER  '  of  the  present  month  (April) 


216  A   BUDGET   OF  PAKADOXES. 

p.  153,  for  the  *  Debates  in  Parliament,'  respecting  the  BISHOP  OP 
JERUSALEM,  viz.  Dr.  Bowring,  Mr.  Hume,  Sir  R.  Inglis,  Sir  R.  Peel, 
Viscount  Palmerston." 

I  have  quoted  this  at  length,  to  show  the  awful  threats  which 
were  published  at  a  time  of  some  little  excitement  about  the 
phenomenon,  under  the  name  of  the  London  Society.  The 
assumption  of  a  corporate  appearance  is  a  very  unfair  trick  :  and 
there  are  junctures  at  which  harm  might  be  done  by  it. 

Wealth  the  name  and  number  of  the  Beast,  666,  in  the  Book  of 
Revelation.     [By  John  Taylor.]     London,  1844,  8vo. 

Whether  Junius  or  the  Beast  be  the  more  difficult  to  identify, 
jmusi)  be  referred  to  Mr.  Taylor,  the  only  person  who  has  at- 
tempted both.  His  cogent  argument  on  the  political  secret  is 
not  unworthily  matched  in  his  treatment  of  the  theological 
riddle.  He  sees  the  solution  in  svTropia,  which  occurs  in  the 
'Acts  of  the  Apostles  as  the  word  for  wealth  in  one  of  its  most 
.disgusting  forms,  and  makes  666  in  the  most  straightforward 
way.  This  explanation  has  as  good  a  chance  as  any  other.  The 
work  contains  a  general  attempt  at  explanation  of  the  Apoca- 
lypse, and  some  history  of  opinion  on  the  subject.  It  has  not 
sthe  prolixity  which  is  so  common  a  fault  of  apocalyptic  com- 
mentators. 

A  practical  Treatise  on  Eclipses  .  .  .  with  remarks  on  the  anom- 
alies of  the  present  Theory  of  the  Tides.    By  T.  Kerigan,  F.R.S. 

1844,  8vo. 

Containing  also  a  refutation  of  the  theory  of  the  tides,  and  after- 
wards increased  by  a  supplement,  '  Additional  facts  and  argu- 
ments against  the  theory  of  the  tides,'  in  answer  to  a  short  notice 
in  the  Athenceum  journal.  Mr.  Kerigan  was  a  lieutenant  in  the 
Navy:  he  obtained  admission  to  the  Royal  Society  just  before 
the  publication  of  his  book. 

A  new  theory  of  Gravitation.      By  Joseph  Denison,  Esq.    London, 

1844,  12mo. 
Commentaries  on  the  Principia.     By  the  author  of  '  A  new  theory 

of  Gravitation.'     London,  1846,  8vo. 

Honour  to  the  speculator  who  can  be  put  in  his  proper  place 
by  one  sentence,  be  that  place  where  it  may. 

'  But  we  have  shown  that  the  velocities  are  inversely  as  the  square 
roots  of  the  mean  distances  from  the  sun  ;  wherefore,  by  equality  of 
ratios,  the  forces  of  the  sun's  gravitation  upon  them  are  also  inversely 
aa  the  square  roots  of  their  distances  from  the  sun.' 


EASTER  DAY  PARADOXERS.  217 

In  the  years  1818  and  1845  the  full  moon  fell  on  Easter  Day, 
having  been  particularly  directed  to  fall  before  it  in  the  act  for 
the  change  of  style,  and  in  the  English  missals  and  prayer-books 
of  all  time  :  perhaps  it  would  be  more  correct  to  say  that  Easter 
Day  was  directed  to  fall  after  the  full  moon  ;  c  but  the  principle 
is  the  same.'  No  explanation  was  given  in  1818,  but  Easter  was 
kept  by  the  tables,  in  defiance  of  the  rule,  and  of  several  protests. 
A  chronological  panic  was  beginning  in  December  1844,  which 
was  stopped  by  the  Times  newspaper  printing  extracts  from  an 
article  of  mine  in  the  Companion  to  the  Almanac  for  1845,  which 
had  then  just  appeared.  No  one  had  guessed  the  true  reason, 
which  is  that  the  thing  called  the  moon  in  the  Gregorian  Calendar 
is  not  the  moon  of  the  heavens,  but  a  fictitious  imitation  put 
wrong  on  purpose,  as  will  presently  appear,  partly  to  keep  Easter 
out  of  the  way  of  the  Jews'  Passover,  partly  for  convenience  of 
calculation.  The  apparent  error  happens  but  rarely  ;  and  all  the 
work  will  perhaps  have  to  be  gone  over  next  time.  I  now  give 
two  bits  of  paradox. 

Some  theologians  were  angry  at  this  explanation.  A  review 
called  the  Christian  Observer  (of  which  Christianity  I  do  not 
know)  got  up  a  crushing  article  against  me.  I  did  not  look  at  it, 
feeling  sure  that  an  article  on  such  a  subject  which  appeared  on 
January  1,  1845,  against  a  publication  made  in  December  1844, 
must  be  a  second-hand  job.  But  some  years  afterwards  (Sept.  10, 
1850),  the  reviews,  &c.  having  been  just  placed  at  the  disposal  of 
readers  in  the  old  reading-  room  of  the  Museum,  I  made  a  tour  of 
inspection,  came  upon  my  critic  on  his  perch,  and  took  a  look  at 
him.  I  was  very  glad  to  remember  this,  for,  though  expecting 
only  second-hand,  yet  even  of  this  there  is  good  and  bad ;  and 
I  expected  to  find  some  hints  in  the  good  second-hand  of  a 
respectable  clerical  publication.  I  read  on,  therefore,  attentively, 
but  not  long  :  I  soon  came  to  the  information  that  some  additions 
to  Delambre's  statement  of  the  ride  for  finding  Easter,  belonging 
to  distant  years,  had  been  made  by  Sir  Harris  Nicolas !  Now  as  I 
myself  furnished  my  friend  Sir  H.  N.  with  Delambre's  digest  of 
Clavius's  rule,  which  I  translated  out  of  algebra  into  common 
language  for  the  purpose,  I  was  pretty  sure  this  was  the  ignorant 
reading  of  a  person  to  whom  Sir  H.  N.  was  the  highest  ariik- 
metical  authority  on  the  subject.  A  person  pretending  to 
chronology,  without  being  able  to  distinguish  the  historical 
points — so  clearly  as  they  stand  out — in  which  Sir  H.  N.  speaks 
with  authority,  from  the  arithmetical  points  of  pure  reckoning  on 
which  he  does  not  pretend  to  do  more  than  directly  repeat  others, 


213  A   BUDGET   OF  PAEADOXES. 

.must  be  as  fit  to  talk  about  the  construction  of  Easter  Tables  as 
the  Spanish  are  to  talk  French.  I  need  hardly  say  that  the 
additions  for  distant  years  are  as  much  from  Clavius  as  the  rest : 
my  reviewer  was  not  deep  enough  in  his  subject  to  know  that 
Clavius  made  and  published,  from  his  rules,  the  full  table  up  to 
A.D.  5000,  for  all  the  moveable  feasts  of  every  year !  I  gave  only 
a  glance  at  the  rest :  I  found  I  was  either  knave  or  fool,  with  a 
leaning  to  the  second  opinion ;  and  I  came  away  satisfied  that  my 
critic  was  either  ignoramus  or  novice,  with  a  leaning  to  the  first. 
I  afterwards  found  an  ambiguity  of  expression  in  Sir  H.  N.'s 
account — whether  his  or  mine  I  could  not  tell — which  might 
mislead  a  novice  or  content  an  ignoramus,  but  would  have  been 
properly  read  or  further  inquired  into  by  a  competent  person. 

The  second  case  is  this.  Shortly  after  the  publication  of  my 
article,  a  gentleman  called  at  my  house,  and,  finding  I  was  not  at 
home,  sent  up  his  card — with  a  stylish  west-end  club  on  it — to 
my  wife,  begging  for  a  few  words  on  pressing  business.  With 
many  well-expressed  apologies,  he  stated  that  he  had  been  alarmed 
by  hearing  that  Prof.  De  M.  had  an  intention  of  altering  Easter 
next  year.  Mrs.  De  M.  kept  her  countenance,  and  assured  him 
that  I  had  no  such  intention,  and  further,  that  she  greatly 
doubted  my  having  the  power  to  do  it.  Was  she  quite  sure? 
his  authority  was  very  good :  fresh  assurances  given.  He  was 
greatly  relieved,  for  he  had  some  horses  training  for  after  Easter, 
which  would  not  be  ready  to  run  if  it  were  altered  the  wrong 
way.  A  doubt  comes  over  him  :  would  Mrs.  De  M.,  in  the  event 
;  of  her  being  mistaken,  give  him  the  very  earliest  information  ? 
Promise  given ;  profusion  of  thanks ;  more  apologies ;  and  de- 
parture. 

Now,  candid  reader ! —  or  uncandid  either  ! — which  most 
deserves  to  be  laughed  at  ?  A  public  instructor,  who  undertakes 
to  settle  for  the  world  whether  a  reader  of  Clavius,  the  constructor 
of  the  Gregorian  Calendar,  is  fool  or  knave,  upon  information 
derived  from  a  compiler — in  this  matter — of  his  own  day;  or  a 
gentleman  of  horse  and  dog  associations  who,  misapprehending 
something  which  he  heard  about  a  current  topic,  infers  that  the 
reader  of  Clavius  had  the  ear  of  the  Government  on  a  proposed 
alteration.  I  suppose  the  querist  had  heard  some  one  say, 
perhaps,  that  the  day  ought  to  be  set  right,  and  some  one  else 
remark  that  I  might  be  consulted,  as  the  only  person  who  had 
discussed  the  matter  from  the  original  source  of  the  Calendar. 

To  give  a  better  chance  of  the  explanation  being  at  once 
produced,  next  time  the  real  full  moon  and  Easter  Day  shall  fall 


THE   EASTER   QUESTION.'  219 

together,  I  insert  here  a  summary  which  was  printed  in  the  Irish 
Prayer-book  of  the  Ecclesiastical  Society.  If  the  amusement 
given  by  paradoxers  should  prevent  a  useless  discussion  some  years 
hence,  I  and  the  paradoxers  shall  have  done  a  little  good  between 
us — at  any  rate,  I  have  done  my  best  to  keep  the  heavy  weight 
afloat  by  tying  bladders  to  it.  I  think  the  next  occurrence  will 
be  in  1875. 

EASTER   DAY. 

In  the  years  1818  and  1845,  Easter  Day,  as  given  by  the  rules  in 
24  Geo.  II.  cap.  23.  (known  as  the  act  for  the  change  of  style)  contra- 
dicted the  precept  given  in  the  preliminary  explanations.  The  precept 
is  as  follows  : — 

'  Easter  Day,  on  which  the  rest '  of  the  moveable  feasts  '  depend,  is 
always  the  First  Sunday  after  the  Full  Moon,  which  happens  upon  or 
next  after  the  Twenty-first  Day  of  March  ;  and  if  the  Full  Moon  hap- 
pens upon  a  Sunday,  Easter  Day  is  the  Sunday  after.' 

But  in  1818  and  1845,  the  full  moon  fell  on  a  Sunday,  and  yet  the 
rules  gave  that  same  Sunday  for  Easter  Day.  Much  discussion  was 
produced  by  this  circumstance  in  1818  :  but  a  repetition  of  it  in  1845 
was  nearly  altogether  prevented  by  a  timely l  reference  to  the  inten- 
tion of  those  who  conducted  the  Gregorian  reformation  of  the  Calendar. 
Nevertheless,  seeing  that  the  apparent  error  of  the  Calendar  is  due  to 
the  precept  in  the  Act  of  Parliament,  which  is  both  erroneous  and  in- 
sufficient, and  that  the  difficulty  will  recur  so  often  as  Easter  Day  falls 
on  the  day  of  full  moon,  it  may  be  advisable  to  select  from  the  two 
articles  cited  in  the  note  sucb  of  their  conclusions  and  rules,  without 
proof  or  controversy,  as  will  enable  the  reader  to  understand  the  main 
points  of  the  Easter  question,  and,  should  he  desire  it,  to  calculate  for 
himself  the  Easter  of  the  old  or  new  style,  for  any  given  year. 

] .  In  the  very  earliest  age  of  Christianity,  a  controversy  arose  as 
to  the  mode  of  keeping  Easter,  some  desiring  to  perpetuate  the  Passover, 
others  to  keep  the  festival  of  the  Resurrection.  The  first  afterwards 
obtained  the  name  of  Quartadecimans,  from  their  Easter  being  always 
kept  on  ike  fourteenth  day  of  the  moon  (Exod.  xii.  18,  Levit.  xxiii.  5.). 
But  though  it  is  unquestionable  that  a  Judaizing  party  existed,  it  is 
also  likely  that  many  dissented  on  chronological  grounds.  It  is  clear 
that  no  perfect  anniversary  can  take  place,  except  when  the  fourteenth 

1  In  the  Companion  to  the  Almanac  for  1845  is  a  paper  by  Professor  De  Morgan, 
'  On  the  Ecclesiastical  Calendar,'  the  statements  of  which,  so  far  as  concerns  the 
Gregorian  Calendar,  are  taken  direct  from  the  work  of  Clavius,  the  principal  agent  in 
the  arrangement  of  the  reformed  reckoning.  This  was  followed,  in  the  Companion  to 
the  Almanac  for  1846,  by  a  second  paper,  by  the  same  author,  headed  'On  the  Earliest 
Printed  Almanacs,'  much  of  which  is  written  in  direct  supplement  to  the  former 
article. 


220  A   BUDGET   OF  PARADOXES. 

of  the  moon,  and  with  it  the  passover,  falls  on  a  Friday.  Suppose,  for 
instance,  it  falls  on  a  Tuesday :  one  of  three  things  must  be  done. 
Either  (which  seems  never  to  have  been  proposed)  the  crucifixion  and 
resurrection  must  be  celebrated  on  Tuesday  and  Sunday,  with  a  wrong 
interval ;  or  the  former  on  Tuesday,  the  latter  on  Thursday,  aban- 
doning the  first  day  of  the  week  ;  or  the  former  on  Friday,  and  the 
latter  on  Sunday,  abandoning  the  paschal  commemoration  of  the 
crucifixion. 

The  last  mode  has  been,  as  every  one  knows,  finally  adopted.  The 
disputes  of  the  first  three  centuries  did  not  turn  on  any  calendar 
questions.  The  Easter  question  was  merely  the  symbol  of  the  strug- 
gle between  what  we  may  call  the  Jewish  and  Gentile  sects  of 
Christians  :  and  it  nearly  divided  the  Christian  world,  the  Easterns, 
for  the  most  part,  being  Quartadecimans.  It  is  very  important  to 
note  that  there  is  no  recorded  dispute  about  a  method  of  predicting  the 
new  moon,  that  is,  no  general  dispute  leading  to  formation  of  sects : 
there  may  have  been  difficulties,  and  discussions  about  them.  The 
Metonic  cycle,  presently  mentioned,  must  have  been  used  by  many, 
perhaps  most,  churches. 

2.  The  question  came  before  the  Nicene  Council  (A.D.  325)  not 
as  an  astronomical,  but  as  a  doctrinal,  question :  it  was,  in  fact,  this, 
Shall  the  passover  l  be  treated  as  a  part  of  Christianity  ?  The  Council 
resolved  this  question  in  the  negative,  and  the  only  information  on  its 
premises  and  conclusion,  or  either,  which  comes  from  itself,  is  contained 
in  the  following  sentence  of  the  synodical  epistle,  which  epistle  is  pre- 
.  served  by  Socrates  and  Theodoret.  '  We  also  send  you  the  good  news 
concerning  the  unanimous  consent  of  all  in  reference  to  the  celebration 
of  the  most  solemn  feast  of  Easter,  for  this  difference  also  has  been 
made  up  by  the  assistance  of  your  prayers  :  so  that  all  the  brethren  in 
the  East,  who  formerly  celebrated  this  festival  at  the  same  time  as  the 
Jews,  will  in  future  conform  to  the  Romans  and  to  us,  and  to  all  who 
have  of  old  observed  our  manner  of  celebrating  Easter.'  This  is  all 
that  can  be  found  on  the  subject :  none  of  the  stories  about  the  Coun- 
cil ordaining  the  astronomical  mode  of  finding  Easter,  and  introducing 
the  Metonic  cycle  into  ecclesiastical  reckoning,  have  any  contemporary 
evidence :  the  canons  which  purport  to  be  those  of  the  Nicene  Council 
do  not  contain  a  word  about  Easter  ;  and  this  is  evidence,  whether  we 
suppose  those  canons  to  be  genuine  or  spurious. 

3.  The  astronomical  dispute  about  a  lunar  cycle  for  the  predic- 
tion of  Easter  either  commenced,  or  became  prominent,  by  the  ex- 
tinction of  greater  ones,  soon  after  the  time  of  the  Nicene  Council. 
Pope  Innocent  I.  met  with  difficulty  in  414.  S.  Leo,  in  454,  ordained 
that  Easter  of  455  should  be  April  24 ;  which  is  right.  It  is  useless  to 

1  It  may  be  necessary  to  remind  some  English  readers  that  in  Latin  and  its  derived 
European  languages,  -what  we  call  Easter  is  called  the  passover  (pascha).  The 
Quartadecimans  had  the  name  on  their  side :  a  possession  which  often  is,  in  this  world, 
nine  points  of  the  law. 


THE  EASTEK  QUESTION.  221 

record  details  of  these  disputes  in  a  snmmary :  the  result  was,  that  in 
the  year  463,  Pope  Hilarius  employed  Victorinus  of  Aquitaine  to 
correct  the  Calendar,  and  Victorinus  formed  a  rule  which  lasted  until 
the  sixteenth  century.  He  combined  the  Metonic  cycle  and  the  solar 
cycle,  presently  described.  But  this  cycle  bears  the  name  of  Dionysius 
Exiguus,  a  Scythian  settled  at  Rome,  about  A.D.  530,  who  adapted 
it  to  his  new  yearly  reckoning,  when  he  abandoned  the  eera  of  Dio- 
cletian as  a  commencement,  and  constructed  that  which  is  now  in 
common  use. 

4.  With  Dionysius,  if  not  before,  terminated  all  difference  as   to 
the  mode  of  keeping  Easter  which  is  of  historical  note  :  the  increasing 
defects  of  the   Easter  Cycle  produced   in  time  the  remonstrance  of 
persons  versed  in  astronomy,  among  whom  may  be  mentioned  Roger 
Bacon,   Sacrobosco,   Cardinal  Cusa,   Regiomontanus,    &c.      Prom  the 
middle  of  the  sixth  to  that  of  the  sixteenth  century,  one  rule  was 
observed. 

5.  The  mode  of  applying   astronomy   to    chronology  has   always 
involved   these    two   principles.      First,   the   actual    position   of    the 
heavenly  body  is  not  the  object  of  consideration,  but  what  astronomers 
call  its  mean  place,  which  may  be  described  thus.     Let  a  fictitious  sun 
or  moon  move  in  the  heavens,  in  such  manner  as  to  revolve  among  the 
fixed  stars  at  an  average  rate,  avoiding  the  alternate  accelerations  and 
retardations  which  take  place  in  every  planetary  motion.     Thus  the 
fictitious   (say  mean)   sun  and  moon  are  always  very  near  to  the  real 
sun  and  moon.     The  ordinary  clocks  show  time  by  the  mean,  not  the 
real,  sun :  and  it  was  always  laid  down  that  Easter  depends  on  the 
opposition  (or  full  moon)  of  the  mean  sun  and  moon,  not  of  the  real 
ones.     Thus  we  see  that,  were  the  Calendar  ever  so  correct  as  to  the 
mean  moon,  it  would  be  occasionally  false  as  to  the  true  one  :  if,  for 
instance,  the  opposition  of  the  mean  sun  and  moon  took  place  at  one 
second  before  midnight,  and  that  of  thet  real  bodies  only  two  seconds 
afterwards,  the  calendar  day  of  full  moon  would  be  one  day  before 
that  of  the  common  almanacs.     Here  is  a  way  in  which  the  discussions 
of  1818  and  1845  might  have  arisen:  the  British  legislature   has  de- 
fined the  moon  as  the  regulator  of  the  paschal  calendar.     But  this  was 
only  a  part  of  the  mistake. 

6.  Secondly,  in  the  absence  of  perfectly  accurate  knowledge  of  the 
solar  and  lunar  motion  (and  for  convenience,  even  if  such  knowledge 
existed),  cycles  are,  and  always  have   been   taken,  which   serve   to 
represent  those  motions  nearly.     The  famous  Metonic  cycle,  which  is 
introduced  into  ecclesiastical  chronology  under  the  name  of  the  cycle 
of  the  golden  numbers,  is  a  period  of  19  Julian1  years.     This  period, 
in   the  old  Calendar,  was  taken  to  contain  exactly  235  lunations,  or 
intervals  between  new  moons,  of  the  mean  moon.     Now  the  state  of 
the  case  is  this  : — 

1  The  Julian  year  is  a  year  of  the  Julian  Calendar,  in  which  there  is  leap  year  every 
fourth  year.     Its  average  length  is  therefore  365  days  and  a  quarter. 


222  A   BUDGET   OF  PAEADOXES. 

19  average  Julian  years  make  6939  days  18  hours. 

235  average  lunations  make  6939  days  16  hours  31  minutes. 

So  that  successive  cycles  of  golden  numbers,  supposing  the  first  to 
start  right,  amount  to  making  the  new  moons  fall  too  late,  gradually, 
so  that  the  mean  moon  of  this  cycle  gains  1  hour  29  minutes  in  19 
years  upon  the  mean  moon  of  the  heavens,  or  about  a  day  in  300 
years.  When  the  Calendar  was  reformed,  the  calendar  new  moons 
were  four  days  in  advance  of  the  mean  moon  of  the  heavens :  so  that, 
for  instance,  calendar  full  moon  on  the  18th  usually  meant  real  full 
moon  on  the  14th. 

7.  If    the    difference   above   had   not   existed,  the   moon   of    the 
heavens  (the  mean  moon  at  least),  would  have  returned  permanently 
to  the  same  days  of  the  month  in  19  years ;  with   an  occasional  slip 
arising  from  the   unequal  distribution  of  the  leap  years,  of  which  a 
period  contains  sometimes  five  and  sometimes  four.     As  a  general  rule, 
the  days  of  new  and  full  moon  in  any  one  year  would  have  been  also 
the  days  of  new  and  full  moon  of  a  year  having  19  more  units  in  its 
date.     Again,  if  there  had  been  no  leap  years,  the  days  of  the  month 
would  have  returned  to  the  same  days  of  the  week  every  seven  years. 
The  introduction  of  occasional  29ths  of  February  disturbs  this,  and 
makes  the  permanent  return  of  month  days  to  week  days  occur  only 
after  28  years.     If  all  had  been  true,  the  lapse  of  28  times  19,  or  532 
years,  would  have  restored  the  year  in  every  point :  that  is,  A.D.  1,  for 
instance,  and  A.D.   538,  would  have  had  the  same  almanac  in  every 
matter  relating  to  week  days,  month  days,  sun,  and  moon  (mean  sun 
and  moon  at  least).     And  on  the  supposition  of  its  truth,  the  old 
system  of  Dionysius  was  framed.     Its  errors  are,  first,  that  the  mo- 
ments of  mean  new  moon  advance  too  much  by  Ih.  29m.  in  19  average 
Julian  years ;  secondly,  that  the  average  Julian  year  of  365^  days  is 
too  long  by  llm.  10s. 

8.  The   Council  of  Trent,  moved  by  the  representations  made  on 
the  state  of  the  Calendar,  referred  the  consideration  of  it  to  the  Pope- 
In  1577,  Gregory  XIII.  submitted  to  the  Roman  Catholic  Princes  and 
Universities  a  plan  presented  to  him  by  the  representatives  of  Aloysius 
Lilius,  then  deceased.     This  plan  being  approved  of,  the  Pope  nomi 
nated  a  commission  to  consider  its  details,  the  working  member  of 
which  was  the  Jesuit  Clavius.     A  short  work  was  prepared  by  Clavius, 
descriptive  of  the  new   Calendar:  this  was  published1  in  1582,  with 
the  Pope's  bull  (dated  February  24,  1581)  prefixed.     A  larger  work 
was  prepared  by  Clavius,  containing  fuller  explanation,  and  entitled 
'  Romani  Calendarii  a  Gregorio  XIII.  Pontifice  Maximo  restituti  Ex- 
plicatio.'     This  was  published  at  Rome  in  1603,  and  again  in  the  col- 
lection of  the  works  of  Clavius  in  1612. 

1  The  title  of  this  work,  which  is  the  authority  on  all  points  of  the  new  Calendar,  is 
1  Kalendarium  Gregorianum  Perpetuum.  Cum  Privilegio  Summi  Pontificis  Et  Alio- 
rum  Principum.  Komse,  Ex  Officina  Dominici  Basse.  MDLXXXII.  Cum  Licentia, 
Superiorum '  (quarto,  pp.  60). 


THE  EASTER  QUESTION.    '  223 

9.  The  following  extracts  from  Clavius  settle  the  question  of  the-' 
meaning  of  the  term  moon,  as  used  in  the  Calendar  : — 

*  Who,  except  a  few  who  think  they  are  very  sharp-sighted  in  this 
matter,  is  so  blind  as  not  to  see  that  the  14th  of  the  moon  and  the  full 
moon  are  not  the  same  things  in  the  Church  of  God  ?  .  .  .  Although 
the  Church,  in  finding  the  new  moon,  and  from  it  the  14th  day,  uses 
neither  the  true  nor  the  mean  motion  of  the  moon,  but  measures  only 
according  to  the  order  of  a  cycle,  it  is  nevertheless  undeniable  that 
the  mean  full  moons  found  from  astronomical  tables  are  of  the  greatest 
use  in  determining  the  cycle  which  is  to  be  preferred  .  .  .  the  new 
moons  of  which  cycle,  in  order  to  the  due  celebration  of  Easter,  should 
be  so  arranged  that  the  14th  days  of  those  moons,  reckoning  from  the 
day  of  new  moon  inclusive,  should  not  fall  two  or  more  days  before  the 
mean  full  moon,  but  only  one  day,  or  else  on  the  very  day  itself,  or 
not  long  after.  And  even  thus  far  the  Church  need  not  take  very 
great  pains  ...  for  it  is  sufficient  that  all  should  reckon  by  the  14th 
day  of  the  moon  in  the  cycle,  even  though  sometimes  it  should  be  more 
than  one  day  before  or  after  the  mean  full  moon  .  .  .  We  have  taken 
pains  that  in  our  cycle  the  new  moons  should  follow  the  real  new 
moons,  so  that  the  14th  of  the  moon  should  fall  either  the  day  before 
the  mean  full  moon,  or  on  that  day,  or  not  long  after ;  and  this  was 
done  on  purpose,  for  if  the  new  moon  of  the  cycle  fell  on  the  same  day 
as  the  mean  new  moon  of  the  astronomers,  it  might  chance  that  we 
should  celebrate  Easter  on  the  same  day  as  the  Jews  or  the  Quarta- 
deciman  heretics,  which  would  be  absurd,  or  else  before  them,  which 
would  be  still  more  absurd.' 

From  this  it  appears  that  Clavius  continued  the  Calendar  of  his 
predecessors  in  the  choice  of  the  fourteenth  day  of  the  moon.  Our 
legislature  lays  down  the  day  of  the  full  moon :  and  this  mistake 
appears  to  be  rather  English  than  Protestant ;  for  it  occurs  in  missals 
published  in  the  reign  of  Queen  Mary.  The  calendar  lunation  being 
29^  days,  the  middle  day  is  the  fifteenth  day,  and  this  is  and  was 
reckoned  as  the  day  of  the  full  moon.  There  is  every  right  to  presume 
that  the  original  passover  was  a  feast  of  the  real  full  moon :  but  it  is 
most  probable  that  the  moons  were  then  reckoned,  not  from  the  astro- 
nomical conjunction  with  the  sun,  which  nobody  sees  except  at  an 
eclipse,  but  from  the  day  of  first  visibility  of  the  new  moon.  In  fine 
climates  this  would  be  the  day  or  two  days  after  conjunction ;  and  the 
fourteenth  day  from  that  of  first  visibility  inclusive,  would  very  often 
be  the  day  of  full  moon.  The  following  is  then  the  proper  correction 
of  the  precept  in  the  Act  of  Parliament : — 

Easter  Day,  on  which  the  rest  depend,  is  always  the  First  Sunday 
after  the  fourteenth  day  of  the  calendar  moon  which  happens  upon  or 
next  after  the  Twenty-first  day  of  March,  according  to  the  rules  laid 
down  for  the  construction  of  the  Calendar ;  and  if  the  fourteenth  day 
happens  upon  a  Sunday,  Easter  Day  is  the  Sunday  after. 

10.     Further,  it  appears  that  Clavius  valued  the  celebration  of  the 


224  A   BUDGET  OF  PARADOXES. 

festival  after  the  Jews,  &c.,  more  than  astronomical  correctness.  He 
gives  comparison  tables  which  would  startle  a  believer  in  the  astrono- 
mical intention  of  his  Calendar :  they  are  to  show  that  a  calendar  in 
which  the  moon  is  always  made  a  day  older  than  by  him,  represents  the 
heavens  better  than  he  has  done,  or  meant  to  do.  But  it  must  be  ob- 
served that  this  diminution  of  the  real  moon's  age  has  a  tendency  to 
make  the  English  explanation  often  practically  accordant  with  the 
Calendar.  For  the  fourteenth  day  of  Clavius  is  generally  the  fifteenth 
day  of  the  mean  moon  of  the  heavens,  and  therefore  most  often  that  of 
the  real  moon.  But  for  this,  1818  and  1845  would  not  have  been  the 
only  instances  of  our  day  in  which  the  English  precept  would  have 
contradicted  the  Calendar. 

11.  In  the  construction  of  the  Calendar,  Clavius  adopted  the  ancient 
cycle  of  532  years,  but,  we  may  say,  without  ever  allowing  it  to  run 
out.     At  certain  periods,  a  shift  is  made  from  one  part  of  the  cycle 
into  another.     This  is  done  whenever  what  should  be  Julian  leap  year 
is  made  a  common  year,  as  in  1700,  1800,  1900,  2100,  &c.     It  is  also 
done  at  certain  times  to  correct  the  error  of  Ih.  19m.,  before  referred 
to,  in  each  cycle  of  golden  numbers :  Clavius,  to  meet  his  view  of  the 
amount  of  that  error,  put  forward  the  moon's  age  a  day  8  times  in 
2,500  years.     As  we  cannot  enter  at  full  length  into  the  explanation, 
we  must  content  ourselves  with  giving  a  set  of  rules,  independent  of 
tables,  by  which  the  reader  may  find  Easter  for  himself  in  any  year, 
either  by  the  old  Calendar  or  the  new.     Any  one  who  has  much  oc- 
casion to  find  Easters  and  moveable  feasts  should  procure  Francoaur's !- 
tables. 

1 2.  Rule  for  determining  Easter  Day  of  the  Gregorian  Calendar  in  any 
year  of  the  new  style.     To  the  several  parts  of  the  rule  are  annexed,  by 
way  of  example,  the  results  for  the  year  1849. 

I.  Add  1  to  the  given  year.     (1850). 

II.  Take  the  quotient  of  the  given  year  divided  by  4,  neglecting  the  remainder. 
(462). 

III.  Take  16  from  the  centurial  figures  of  the  given  year,  if  it  can  be  done,  and 

take  the  remainder.     (2). 

IV.  Take  the  quotient  of  III.  divided  by  4,  neglecting  the  remainder.     (0). 
V.  From  the  sum  of  I.,  II.,  and  IV.,  substract  III.     (2310). 

VI.  Find  the  remainder  of  V.  divided  by  7.     (0). 

VII.  Subtract  VI.  from  7  ;  this  is  the  number  of  the  dominical  letter  ^  ?  9  ?  ?F  ? 

I«oo4oo7« 
(7;  dominical  letter  Q-). 

VIII.  Divide  I.  by  19,  the  remainder  (or  19,  if  no  remainder)  is  the  golden  number. 
(7). 

1  '  Manuels-Roret.  Theorie  du  Calendrier  et  collection  de  tous  les  Calendriers  des 
Annees  passees  et  futures. . .  .Par  L.  B.  Francoeur, . .  .Paris,  a  la  librairie  encyclope- 
dique  de  Roret,  rue  Hautefeuille,  10  bis.  1842.'  (12mo.)  In  this  valuable  manual, 
the  35  possible  almanacs  are  given  at  length,  with  such  preliminary  tables  as  will 
enable  any  one  to  find,  by  mere  inspection,  which  almanac  he  is  to  choose  for  any 
year,  whether  of  old  or  new  style.  [1866.  I  may  now  refer  to  my  own  'Book  of 
Almanacs,'  for  the  same  purpose]. 


RULE   FOR   FINDING   EASTER   DAY. 


225 


IX.  From  the  centurial  figures  of  the  year  subtract  17,  divide  by  25,  and  keep  the 

quotient.     (0). 

X.  Subtract  IX.  and  15  from  the  centurial  figures,  divide  by   3,  and  keep  the 
quotient.     (1). 

XI.  To  VIII.  add  ten  times  the  next  less  number,  divide  by  30,  and  keep  the 

remainder.     (7). 

XII.  To  XI.  add  X.  and  IV.,  and  take  away  III.,  throwing  out  thirties,  if  any.  If 
this  give  24,  change  it  into  25.  If  25,  change  it  into  26,  whenever  the 
golden  number  is  greater  than  11.  If  0,  change  it  into  30.  Thus  we  have 
the  epact,  or  age  of  the  Calendar  moon  at  the  beginning  of  tho  year.  (6). 

When  the  Epact  is  23,  or  less.  \         When  the  Epact  is  greater  than  23. 

XIII.  Subtract  XII.,  the  epact,  from  45.       XIU.  Subtract   XII.,    the    epact,    from 


(39). 

XIV.  Subtract  the  epact  from  27,  divide 
by  7,  and  keep  the  remainder,  or 
7,  if  there  be  no  remainder.  (7). 


75. 

XIV.  Subtract  the  epact  from  57,  divide 
by  7,  and  keep  the  remainder, 
or  7,  if  there  be  no  remainder. 


XV.  To  XIII.  add  VII.,  the  dominical  number,  (and  7  besides,  if  XIV.  be  greater 
than  VII.,)  and  subtract  XIV.,  the  result  is  the  day  of  March,  or  if  more 
than  31,  subtract  31,  and  the  result  is  the  day  of  April,  on  which  Easter 
Sunday  falls.  (39 ;  Easter  Day  is  April  8). 

In  the  following  examples,  the  several  results  leading  to  the  final  con- 
clusion are  tabulated. 


Given  year 

1592 

1637 

1723 

1853 

2018 

4686 

I. 

1593 

1638 

1724 

1854 

2019 

4687 

II. 

398 

409 

430 

463 

504 

1171 

III. 

— 

0 

1 

2 

4 

30 

IV. 

— 

0 

0 

0 

1 

r    7 

V. 

1991 

2047 

2153 

2315 

2520 

5835 

VI. 

3 

3 

4 

5 

0 

4 

VII. 

4 

4 

3 

2 

7 

3 

VIII. 

16 

4 

14 

11 

5 

13 

IX. 

— 

— 

0 

0 

0 

1 

X. 

0 

0 

0 

1 

1 

10 

XI. 

16 

4 

24 

21 

15 

13 

XII. 

16 

4 

23 

20 

13 

0  say  30 

XIII. 

29 

41 

22 

25 

32 

45 

XIV. 

4 

2 

4 

7 

7 

6 

XV. 

29 

43 

28 

27 

32 

49 

Easter  Day. 

Mar.  29 

Apr.  12 

Mar.  28 

Mar.  27 

Apr.  1 

Apr.  18 

13.  Stile  for  determining  Easter  Day  of  the  Antegregorian  Calendar  in 
any  year  of  the  old  style.  To  the  several  parts  of  the  rule  are  annexed, 
by  way  of  example,  the  results  for  the  year  1287.  The  steps  are 
numbered  to  correspond  with  the  steps  of  the  Gregorian  rule,  so  that 
it  can  be  seen  what  augmentations  the  latter  requires. 

I.  Set  down  the  given  year.     (1287). 

II.  Take  the  quotient  of  the  given  year  divided  by  4,  neglecting  the  remainder 
(321). 

V.  Take  4  more  than  the  sum  of  I.  and  II.     (1612). 
VI.  Find  the  remainder  of  V.  divided  by  7.     (2). 

VII.  Subtract  VI.  from  7  ;  this  is  the  number  of  the  dominical  letter 
(5  ;  dominical  letter  E), 

Q 


- 

o  4  o  6  7 


226  A  BUDGET  OF  PAEADOXES. 

VIII.  Divide  one  more  than  the  given  year  by  19,  the  remainder  (or  19  if  no  re- 
mainder) is  the  golden  number.  (15). 

XII.  Divide  3  less  than  11  times  VIII.  by  30  ;  the  remainder  (or  30  if  there  be  no 
remainder)  is  the  epact.  (12). 


When  the  Epact  is  23,  or  less, 

XIII.  Subtract  XII.,  the  epact,  from  45. 

(33). 

XIV.  Subtract  the  epact,  from  27,  divide 

by  7,  and  keep  the  remainder,  or 
7,  if  there  be  no  remainder.  (1). 


When  the  Epact  is  greater  than  23. 

XIII.  Subtract    XII.,    the   epact,  from 

75. 

XIV.  Subtract  the  epact  from  57,  divide 

by  7,  and  keep  the  remainder, 
or  7,  if  there  be  no  remainder. 


XV.  To  XIII.  add  VII.,  the  dominical  number,  (and  7  besides  if  XIV.  be  greater 
than  VII.,)  and  subtract  XIV.,  the  result  is  the  day  of  March,  or  if  more 
than  31,  subtract  31,  and  the  result  is  the  day  of  April,  on  which  Easter 
Sunday  (old  style)  falls.  (37  ;  Easter  Day  is  April  6). 

These  rules  completely  represent  the  old  and  new  Calendars,  so  far 
as  Kaster  is  concerned.  For  further  explanation  we  must  refer  to  the 
articles  cited  at  the  commencement. 

The  annexed  is  the  table  of  new  and  full  moons  of  the 
Gregorian  Calendar,  cleared  of  the  errors  made  for  the  purpose 
of  preventing  Easter  from  coinciding  with  the  Jewish  Passover. 

The  second  table  (page  228)  contains  epacts,  or  ages  of  the 
moon  at  the  beginning  of  the  year  :  thus  in  191  3,  the  epact  is  22  : 
in  1868  it  is  6.  This  table  goes  from  1850  to  1999  :  should  the 
New  Zealander  not  have  arrived  by  that  time,  and  should  the 
churches  of  England  and  Rome  then  survive,  the  epact  table  may 
be  continued  from  their  liturgy-books.  The  way  of  using  the  table 
is  as  follows  :  Take  the  epact  of  the  required  year,  and  find  it 
in  the  farst  or  last  column  of  the  first  table,  in  line  with  it  are 
seen  the  calendar  days  of  new  and  full  moon.  Thus,  when  the 
epact  is  17,  the  new  and  full  moons  of  March  fall  on  the  13th 
and  28th.  The  result  is,  for  the  most  part,  correct :  but  in  a 
minority  of  cases  there  is  an  error  of  a  day.  When  this  happens, 
the  error  is  almost  always  a  fraction  of  a  day  much  less  than 
twelve  hours.  Thus,  when  the  table  gives  full  moon  on  the  27th, 
and  the  real  truth  is  the  28th,  we  may  be  sure  it  is  early  on 
the  28th.  For  example,  the  year  1867.  The  epact  is  25,  and 
we  find  in  the  table  : 

J.          F.    M.        Ap.    M.         Ju.      Jl,        Au.      S.  0.      N.      D. 

New.     .     .      5+      4       5+4       3+2     1,31     29     28-     27     26     25 
Full  ...    20       19-20       19-18         17    16       15     13-      13     11  +  11 

When  the  truth  is  the  day  after  -f  is  written  after  the  date ; 
when  the  day  before,  —  .  Thus,  the  new  moon  of  March  is  on 
the  6th  ;  the  full  moon  of  April  is  on  the  18th. 


Table  of  New  and  Full  ^^ou». 


Jan. 

Feb. 

Mar. 

Apr. 

May 

June 

July 

A.ug. 

Sep. 

Oct. 

NOT. 

Dec. 

1   (I   H 

27 
13 

29 

14 

27 
13 

27 
12 

25 
11 

25 
10 

23 
9 

22 
7 

21 
7 

20 
5 

ll   \}     1 

»{|S 

26 
12 

28 
13 

26 
12 

26 
11 

24 
10 

24 
9 

22 
8 

21 
6 

20 
6 

19 
4 

]4    }    2 

3{ 

27 
12 

25 
11 

27 
12 

25 
11 

25 
10 

23 
9 

23 
8 

21 

7 

20 
5 

19 
5 

18 
3 

17 
3 

}    3 

4  { 

26 
11 

24 
10 

26 
11 

24 
10 

24 
9 

22 
8 

22 
7 

20 
6 

19 
4 

18 
4 

17 

2 

16 

2,31 

}    * 

5  { 

25 
10 

23 
9 

25 
10 

23 
9 

23 
8 

21 

7 

21 
6 

19 
5 

18 
3 

17 
3 

16 
1 

15 
1,30 

I       e 
/ 

6  { 

24 
9 

22 
8 

2i 
9 

22 
8 

22 
7 

20 
6 

20 
5 

18 
4 

17 
2 

16 

2,31 

15 
30 

29     }     6 

7  { 

23 
8 

21 
7 

23 
8 

21 

7 

21 
6 

19 
5 

19 
4 

17 
3 

16 
1 

15 
1,30 

14 

29 

31}  * 

8  {|  27 

20 
6 

22 

7 

20 
6 

20 
5 

18 
4 

18 
3 

16 
2,31 

15 
30 

14 

29 

13 
28 

SI 

11 

26 

}      8 

9  (|  26 

19 
5 

21 
6 

19 
5 

19 
4 

17 
3 

17 

2 

15 
1.30 

14 

29 

13 
28 

12 
27 

1    9 
J    y 

10  { 

20 
5 

18 
4 

20 
5 

18 
4 

18 
3 

16 
2 

16 
1,31 

1! 
29 

13 
28 

12 

27 

11 
26 

251   |}   10 

11  { 

19 
4 

17 
3 

19 

4 

17 
3 

17 

2 

15 
1,30 

15 

30 

13 

28 

12 

27 

11 
26 

10 
25 

9   \\   11 
24  \j    Ai 

12  {|  '5 

16 
2 

18 
3 

16 
2 

16 
1,31 

14 
29 

14 
29 

12 
27 

11 
26 

10 
25 

9 

24 

23   |}    12 

13  { 

17 
2 

15 
1 

17 
2 

15 
1,30 

15 
30 

13 
28 

13 
28 
12 
27 

11 
26 

10 
25 

9 
24 

8 
23 

7  \\  13 

22      |     *o 

M{ 

16 
1,31 

14 

16 
1,31 

14 
29 

14 

29 

12 
27 

10 

25 

9 
24 

8 
23 

22 

dfe 

15  { 

15 
30 

13 
28 

15 
30 

13 
28 

13 

28 

11 
26 

11 
26 

9 
24 

8 
23 

7 
22 

6 
21 

5 

20 

}  15 

16  { 

14 
29 

12 
27 

14 

29 

12 
27 

12 
27 

10 
25 

10 
25 

8 
23 

7 

22 

6 
21 

5 
20 

4 
19 

}  16 

17  { 

13 

28 

11 
26 

13 

28 

11 
26 

11 
26 

9 
24 

9 
24 

7 

22 

6 

21 

5 
20 

4 
19 

.8  1}  » 

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Ang.i  Sep. 

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Nov 

1  Dec 

A  BUDGET   OF  PAEADOXES. 


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I  now  introduce  a  small  paradox  of  my  own  :  and  as  I  am  not 
able  to  prove  it,  I  am  compelled  to  declare  that  any  one  who 
shall  dissent  must  be  either  very  foolish  or  very  dishonest,  and 
will  make  me  quite  uncomfortable  about  the  state  of  his  soul. 
This  being  settled  once  for  all,  I  proceed  to  say  that  the  necessity 
of  arriving  at  the  truth  about  the  assertions  that  the  Nicene 
Council  laid  down  astronomical  tests  led  me  to  look  at  Fathers, 
Church  histories,  &c.  to  an  extent  which  I  never  dreamed  of 
before.  One  conclusion  which  I  arrived  at  was,  that  the  Nicene 
Fathers  had  a  knack  of  sticking  to  the  question  which  many  later 
councils  could  not  acquire.  In  our  own  day,  it  is  not  permitted 
to  Convocation  seriously  to  discuss  any  one  of  the  points  which 
are  bearing  so  hard  upon  their  resources  of  defence — the  cursing 
clauses  of  the  Athanasian  Creed,  for  example.  And  it  may  be 
collected  that  the  prohibition  arises  partly  from  fear  that  there  - 
is  no  saying  where  a  beginning,  if  allowed,  would  end.  There 
seems  to  be  a  suspicion  that  debate,  once  let  loose,  would  play 
up  old  Trent  with  the  liturgy,  and  bring  the  whole  book  to  book. 
But  if  any  one  will  examine  the  real  Nicene  Creed,  without  the 
augmentation,  he  will  admire  the  way  in  which  the  framers  stuck 
to  the  point,  and  settled  what  they  had  to  decide,  according  to 


EASTER  AND  PASSOVER— CLAVIUS.  .  229 

their  view  of  it.  With  such  a  presumption  of  good  sense  in 
their  favour,  it  becomes  easier  to  believe  in  any  claim  which  may 
be  made  on  their  behalf  to  tact  or  sagacity  in  settling  any  other 
matter.  And  I  strongly  suspect  such  a  claim  may  be  made  for 
them  on  the  Easter  question. 

I  collect  from  many  little  indications,  both  before  and  after 
the  Council,  that  the  division  of  the  Christian  world  into  Judai- 
cal  and  Grentile,  though  not  giving  rise  to  a  sectarian  distinction 
expressed  by  names,  was  of  far  greater  force  and  meaning  than 
historians  prominently  admit.  I  took  note  of  many  indications 
of  this,  but  not  notes,  as  it  was  not  to  my  purpose.  If  it  were 
so,  we  must  admire  the  discretion  of  the  Council.  The  Easter 
question  was  the  fighting  ground  of  the  struggle :  the  Eastern 
or  Judaical  Christians,  with  some  varieties  of  usage  and  meaning, 
would  have  the  Passover  itself  to  be  the  great  feast,  but  taken  in 
a  Christian  sense  ;  the  Western  or  Gentile  Christians,  would  have 
the  commemoration  of  the  Resurrection,  connected  with  the 
Passover  only  by  chronology.  To  shift  the  Passover  in  time, 
under  its  name,  Pascha,  without  allusion  to  any  of  the  force  of 
the  change,  was  gently  cutting  away  the  ground  from  under  the 
feet  of  the  Conservatives.  And  it  was  done  in  a  very  quiet  way :  no 
allusion  to  the  precise  character  of  the  change  ;  no  hint  that  the 
question  was  about  two  different  festivals:  'all  the  brethren  in 
the  East,  who  formerly  celebrated  this  festival  at  the  same  time 
as  the  Jews,  will  in  future  conform  to  the  Romans  and  to  us.* 
The  Judaizers  meant  to  be  keeping  the  Passover  as  a  Christian 
feast :  they  are  gently  assumed  to  be  keeping,  not  the  Passover, 
but  a  Christian  feast ;  and  a  doctrinal  decision  is  quietly,  but 
efficiently,  announced  under  the  form  of  a  chronological  ordin- 
ance. Had  the  Council  issued  theses  of  doctrine,  and  excom- 
municated all  dissentients,  the  rupture  of  the  East  and  West 
would  have  taken  place  earlier  by  centuries  than  it  did.  The 
only  place  in  which  I  ever  saw  any  part  of  my  paradox  ad- 
vanced, was  in  an  article  in  the  Examiner  newspaper,  towards 
the  end  of  1866,  after- the  above  was  written. 

A  story  about  Christopher  Clavius,  the  workman  of  the  new 
Calendar.  I  chanced  to  pick  up  '  Albertus  Pighius  Campensis  de 
sequinoctiorum  solsticiorumque  inventione  ....  Ejusdem  de 
ratione  Paschalis  celebrationis,  De  que  Restitutione  ecclesiastic! 
Kalendarii,'  Paris,  1520,  folio.  On  the  title-page  were  decayed 
words  followed  by  ' .  .  hristophor  .  .  C  .  .  ii,  1556  (or  8),'  the 
last  blank  not  entirely  erased  by  time,  but  showing  the  lower 
halves  of  an  I  and  of  an  a,  and  rather  too  much  room  for  a  v. 
It  looked  very  like  E  Libris  Christopher  i  Clavii  1556.  By  the 


230  A   BUDGET   OF  PARADOXES. 

courtesy  of  some  members  of  the  Jesuit  body  in  London,  I 
procured  a  tracing  of  the  signature  of  Clavius  from  Eome,  and 
the  shapes  of  the  letters,  and  the  modes  of  junction  and  disjunc- 
tion, put  the  matter  beyond  question.  Even  the  extra  space 
was  explained ;  he  wrote  himself  Glaums.  Now  in  1556, 
Clavius  was  nineteen  years  old :  it  thus  appears  probable  that 
the  framer  of  the  Gregorian  Calendar  was  selected,  not  merely 
as  a  learned  astronomer,  but  as  one  who  had  attended  to  the 
calendar,  and  to  works  on  its  reformation,  from  early  youth. 
When  on  the  subject  I  found  reason  to  think  that  Clavius  had 
really  read  this  work,  and  taken  from  it  a  phrase  or  two  and  a 
notion  or  two.  Observe  the  advantage  of  writing  the  baptismal 
name  at  full  length. 

The  discovery  of  a  general  resolution  of  all  superior  finite  equa- 
tions, of  every  numerical  both  algebraick  and  transcendent 
form.  By  A.  P.  Vogel,  mathematician  at  Leipzick.  Leipzick 
and  London,  1845,  8vo. 

This  work  is  written  in  the  English  of  a  German  who  has  not 
mastered  the  idiom :  but  it  is  always  intelligible.  It  professes  to 
solve  equations  of  every  degree  '  in  a  more  extent  sense,  and  till 
to  every  degree  of  exactness.'  The  general  solution  of  equations 
of  all  degrees  is  a  vexed  question,  which  cannot  have  the  mys- 
terious interest  of  the  circle  problem,  and  is  of  a  comparatively 
modern  date.  Mr.  Vogel  announces  a  forthcoming  treatise  in 
which  are  resolved  the  '  last  impossibilities  of  pure  mathematics.' 

Elective  Polarity  the  Universal  Agent.  By  Frances  Barbara 
Burton,  authoress  of  '  Astronomy  familiarized,'  '  Physical  As 
tronomy,'  &c.  London,  1845,  8vo. 

The  title  gives  a  notion  of  the  theory.  The  first  sentence 
states,  that  12,500  years  ago  a  Lyrse  was  the  pole-star,  and 
attributes  the  immense  magnitude  of  the  now  fossil  animals  to  a 
star  of  such  'polaric  intensity  as  Vega  pouring  its  magnetic 
streams  through  our  planet.'  Miss  Burton  was  a  lady  of  property, 
and  of  very  respectable  acquirements,  especially  in  Hebrew  ;  she 
was  eccentric  in  all  things. 

1867. — Miss  Burton  is  revived  by  the  writer  of  a  book  on 
meteorology  which  makes  use  of  the  planets :  she  is  one  of  his 
leading  minds. 

In  the  year  1 845  the  old  Mathematical  Society  was  merged  in 
the  Astronomical  Society.  The  circle-squarers,  &c.,  thrive  more 


SPECULATIVE   THOUGHT   IN   ENGLAND.  231 

in  England  than  in  any  other  country :  there  are  most  weeds 
where  there  is  the  largest  crop.  Speculation,  though  not  en- 
couraged by  our  Government  so  much  as  by  those  of  the  Conti- 
nent, has  had,  not  indeed  such  forcing,  but  much  wider  diffusion  : 
few  tanks,  but  many  rivulets.  On  this  point  I  quote  from  the 
preface  to  the  reprint  of  the  work  of  Ramchundra,  which  I 
superintended  for  the  late  Court  of  Directors  of  the  East  India 
Company. — 

'  That  sound  judgment  which  gives  men  well  to  know  what  is  best 
for  them,  as  well  as  that  faculty  of  invention  which  leads  to  develop- 
ment of  resources  and  to  the  increase  of  wealth  and  comfort,  are  both 
materially  advanced,  perhaps  cannot  rapidly  be  advanced  without,  a 
great  taste  for  pure  speculation  among  the  general  mass  of  the  poople, 
down  to  the  lowest  of  those  who  can  read  and  write.  England  is  a 
marked  example.  Many  persons  will  be  surprised  at  this  assertion. 
They  imagine  that  our  country  is  the  great  instance  of  the  refusal  of 
all  unpractical  knowledge  in  favour  of  what  is  useful.  I  affirm,  on  the 
contrary,  that  there  is  no  country  in  Europe  in  which  there  has  been 
so  wide  a  diffusion  of  speculation,  theory,  or  what  other  unpractical 
word  the  reader  pleases.  In  our  country,  the  scientific  society  is 
always  formed  and  maintained  by  the  people ;  in  every  other,  the 
scientific  academy — most  aptly  named — has  been  the  creation  of  the 
government,  of  which  it  has  never  ceased  to  be  the  nursling.  In  all 
the  parts  of  England  in  which,  manufacturing  pursuits  have  given  the 
artisan  some  command  of  time,  the  cultivation  of  mathematics  and 
other  speculative  studies  has  been,  as  is  well  known,  a  very  frequent 
occupation.  In  no  other  country  has  the  weaver  at  his  loom  bent  over 
the  Principia  of  Newton  ;  in  no  other  country  has  the  man,  of  weekly 
wages  maintained  his  own  scientific  periodical.  With,  us,  since  the 
beginning  of  the  last  century,  scores  upon  scores — perhaps  hundreds, 
for  I  am  far  from  knowing  all — of  annuals  have  run,  some  their  ten 
years,  some  their  half-century,  some  their  century  and  a  half,  con- 
taining questions  to  be  answered,  from  which  many  of  our  examiners 
in  the  Universities  have  culled  materials  for  the  academical  contests. 
And  these  questions  have  always  been  answered,  and  in  cases  without 
number  by  the  lower  order  of  purchasers,  the  mechanics,  the  weavers, 
and  the  printers'  workmen.  I  cannot  here  digress  to  point  out  the 
manner  in  which  the  concentration  of  manufactures,  and  the  general 
diffusion  of  education,  have  affected  the  state  of  things  ;  I  speak  of  the 
time  during  which  the  present  system  took  its  rise,  and  of  the  circum- 
stances under  which  many  of  its  most  effective  promoters  were  trained. 
In  all  this  there  is  nothing  which  stands  out,  like  the  state-nourished 
academy,  with  its  few  great  names  and  brilliant  single  achievements. 
This  country  has  differed  from  all  others  in  the  wide  diffusion  of  tho 
disposition  to  speculate,  which  disposition  has  found  its  place  among 
the  ordinary  habits  of  life,  moderate  in  its  action,  healthy  in  its 
amount.' 


232  A  BUDGET  OF  PARADOXES, 

Among  the  most  remarkable  proofs  of  the  diffusion  of  specu- 
lation was  the  Mathematical  Society,  which  flourished  from  1717 
to  1845.  Its  habitat  was  Spitalfields,  and  I  think  most  of  its 
existence  was  passed  in  Crispin  Street,  It  was  originally  a  plain 
society,  belonging  to  the  studious  artisan.  The  members  met  for 
discussion  once  a  week ;  and  I  believe  I  am  correct  in  saying  that 
each  man  had  his  pipe,  his  pot,  and  his  problem.  One  of  their 
old  rules  was  that,  '  If  any  member  shall  so  far  forget  himself  and 
the  respect  due  to  the  Society  as  in  the  warmth  of  debate  to 
threaten  or  offer  personal  violence  to  any  other  member,  he  shall 
be  liable  to  immediate  expulsion,  or  to  pay  such  fine  as  the 
majority  of  the  members  present  shall  decide.'  But  their  great 
rule,  printed  large  on  the  back  of  the  title  page  of  their  last  book 
of  regulations,  was  '  By  the  constitution  of  the  Society,  it  is  the 
•duty  of  every  member,  if  he  be  asked  any  mathematical  or  philo- 
sophical question  by  another  member,  to  instruct  him  in  the 
plainest  and  easiest  manner  he  is  able.'  We  shall  presently  see 
that,  in  old  time,  the  rule  had  a  more  homely  form. 

I  have  been  told  that  De  Moivre  was  a  member  of  this  Society. 
This  I  cannot  verify :  circumstances  render  it  unlikely ;  even 
though  the  French  refugees  clustered  in  Spitalfields  ;  many  of 
them  were  of  the  Society,  which  there  is  some  reason  to  think 
was  founded  by  them.  But  Dollond,  Thomas  Simpson,  Saun- 
derson,  Crossley,  and  others  of  known  name,  were  certainly 
members.  The  Society  gradually  declined,  and  in  1845  was 
reduced  to  nineteen  members.  An  arrangement  was  made  by 
which  sixteen  of  these-  members,  who  were  not  already  in  the 
Astronomical  Society  became  Fellows  without  contribution,  all 
the  books  and  other  property  of  the  old  Society  being  transferred 
,to  the  new  one.  I  was  one  of  the  committee  which  made  the 
•  preliminary  inquiries,  and  the  reason  of  the  decline  was  soon 
.manifest.  The  only  question  which  could  arise  was  whether  the 
.-members  of  the  society  of  working  men — for  this  repute  still 
continued — were  of  that  class  of  educated  men  who  could  as- 
sociate with  the  Fellows  of  the  Astronomical  Society  on  terms 
agreeable  to  all  parties.  We  found  that  the  artisan  element  had 
been  extinct  for  many  years  ;  there  was  not  a  man  but  might,  as 
to  education,  manners,  and  position,  have  become  a  Fellow  in  the 
usual  way.  The  fact  was  that  life  in  Spitalfields  had  become 
harder  :  and  the  weaver  could  only  live  from  hand  to  mouth,  and 
not  up  to  the  brain.  The  material  of  the  old  Society  no  longer 
existed. 


THE   OLD   MATHEMATICAL   SOCIETY.  233 

In  1798,  experimental  lectures  were  given,  a  small  charge  for 
admission  being  taken  at  the  door  :  by  this  hangs  a  tale — and  a 
song.  Many  years  ago,  I  found  among  papers  of  a  deceased  friend, 
who  certainly  never  had  anything  to  do  with  the  Society,  and 
who  passed  all  his  life  far  from  London,  a  song,  headed  '  Song 
sung  at  a  Mathematical  Society  in  London,  at  a  dinner  given  to 
Mr.  Fletcher,  a  solicitor,  who  had  defended  the  Society  gratis.' 
Mr.  Williams,  the  Assistant  Secretary  of  the  Astronomical  Society, 
formerly  Secretary  of  the  Mathematical  Society,  remembered  that 
the  Society  had  had  a  solicitor  named  Fletcher  among  the 
members.  Some  years  elapsed  before  it  struck  me  that  my  old 
friend  Benjamin  Gompertz,  who  had  long  been  a  member,  might 
have  some  recollection  of  the  matter.  The  folio  wing  is  an  extract 
of  a  letter  from  him  (July  9,  1861) : — 

As  to  the  Mathematical  Society,  of  which  I  was  a  member  when 
only  18  years  of  age,  [Mr.  G.  was  born  in  1779],  having  been,  contrary 
to  the  rules,  elected  under  the  age  of  21.  How  I  came  to  be  a 
member  of  that  Society — and  continued  so  until  it  joined  the  Astro- 
nomical Society,  and  was  then  the  President — was :  I  happened  to 
pass  a  bookseller's  small  shop,  of  second-hand  books,  kept  by  a  poor 
taylor,  but  a  good  mathematician,  John  Griffiths.  I  was  very  pleased 
to  meet  a  mathematician,  and  I  asked  him  if  he  would  give  me  some 
lessons  ;  and  his  reply  was  that  I  was  more  capable  to  teach  him,  but 
he  belonged  to  a  society  of  mathematicians,  and  he  would  introduce 
me.  I  accepted  the  offer,  and  I  was  elected,  and  had  many  scholars 
then  to  teach,  as  one  of  the  rules  was,  if  a  member  asked  for  informa- 
tion, and  applied  to  any  one  who  could  give  it,  he  was  obliged  to  give 
it.,  or  fine  one  penny.  Though  I  might  say  much  with  respect  to  the 
Society  which  would  be  interesting,  I  will  for  the  present  reply  only  to 
your  question.  I  well  knew  Mr.  Fletcher,  who  was  a  very  clever  and 
very  scientific  person.  He  did,  as  solicitor,  defend  an  action  brought 
by  an  informer  against  the  Society — I  think  for  5,OOOZ. — for  giving 
lectures  to  the  public  in  philosophical  subjects  [i.e.  for  unlicensed 
public  exhibition  with  money  taken  at  the  doors].  I  think  the  price 
for  admission  was  one  shilling,  and  we  used  to  have,  if  I  rightly 
recollect,  from  two  to  three  hundred  visitors.  Mr.  Fletcher  was  suc- 
cessful in  his  defence,  and  we  got  out  of  our  trouble.  There  was  a 
collection  made  to  reward  his  services,  but  he  did  not  accept  of  any 
reward  :  and  I  think  we  gave  him  a  dinner,  as  you  state,  and  enjoyed 
ourselves  ;  no  doubt  with  astronomical  songs  and  other  songs  ;  but  my 
recollection  does  not  enable  me  to  say  if  the  astronomical  song  was  a 
drinking  song.  I  think  the  anxiety  caused  by  that  action  was  the 
cause  of  some  of  the  members'  death.  [They  had,  no  doubt,  broken 
the  law  in  ignorance ;  and  by  the  sum  named,  the  informer  must  have 
been  present,  and  sued  for  a  penalty  on  every  shilling  he  could  prove 
to  have  been  taken]. 


234  A  BUDGET  OF  PARADOXES. 

I  by  no  means  guarantee  that  the  whole  song  I  proceed  to  give 
is  what  was  sung  at  the  dinner  :  I  suspect,  by  the  completeness  of 
the  chain,  that  augmentations  have  been  made.  My  deceased 
friend  was  just  the  man  to  add  some  verses,  or  the  addition  may 
have  been  made  before  it  came  into  his  hands,  or  since  his  decease, 
for  the  scraps  containing  the  verses  passed  through  several  hands 
before  they  came  into  mine.  We  may,  however,  be  pretty  sure 
that  the  original  is  substantially  contained  in  what  is  given,  and 
that  the  character  is  therefore  preserved.  I  have  had  myself  to 
repair  damages  every  now  and  then,  in  the  way  of  conjectural 
restoration  of  defects  caused  by  ill-usage. 

THE   ASTRONOMER'S   DRINKING-SONG. 

'  WHOE'ER  would  search  the  starry  sky, 

Its  secrets  to  divine,  sir, 
Should  take  Ms  glass — I  mean,  should  try 

A  glass  or  two  of  wine,  sir  ! 
True  virtue  lies  in  golden  mean, 

And  man  must  wet  his  clay,  sir ; 
Join  these  two  maxims,  and  'tis  seen 

He  should  drink  his  bottle  a  day,  sir  ! 

Old  Archimedes,  reverend  sage  ! 

By  trump  of  fame  renowned,  sir, 
Deep  problems  solved  in  every  page, 

And  the  sphere's  curved  surface  found,  sir: 
Himself  he  would  have  far  outshone, 

And  borne  a  wider  sway,  sir, 
Had  he  our  modern  secret  known, 

And  drank  his  bottle  a  day,  sir ! 

When  Ptolemy,  now  long  ago, 

Believed  the  earth  stood  still,  sir, 
He  never  would  have  blundered  so, 

Had  he  but  drunk  his  fill,  sir : 
He'd  then  have  felt1  it  circulate, 

And  would  have  learnt  to  sav,  sir, 

I/    I  9 

The  true  way  to  investigate 

Is  to  drink  your  bottle  a  day,  sir ! 

Copernicus,  that  learned  wight, 

The  glory  of  his  nation, 
With  draughts  of  wine  refreshed  his  sight, 

And  saw  the  earth's  rotation ; 

1  Dr.  Whewell,  when  I  communicated  this  song  to  him,  started  the  opinion,  which 
I  had  before  him,  that  this  was  a  very  good  idea,  of  which  too  little  was  made. 


THE  ASTRONOMER'S   DRINKING-SONG.  235 

Each  planet  then  its  orb  described, 

The  moon  got  under  way,  sir ; 
T^ese  truths  from  nature  he  imbibed 

For  he  drank  his  bottle  a  day,  sir  ! 

The  noble1  Tycho  placed  the  stars, 

Each  in  its  due  location  ; 
He  lost  his  nose2  by  spite  of  Mars, 

Bnt  that  was  no  privation  : 
Had  he  but  lost  his  mouth,  I  grant 

He  would  have  felt  dismay,  sir, 
Bless  you  !  Tie  knew  what  he  should  want 

To  drink  his  bottle  a  day,  sir  ! 

Cold  water  makes  no  lucky  hits ; 

On  mysteries  the  head  runs  : 
Small  drink  let  Kepler  time  his  wits 

On  the  regular  polyhedrons  : 
He  took  to  wine,  and  it  changed  the  chime, 

His  genius  swept  away,  sir, 
Through  area  varying  3  as  the  time 

At  the  rate  of  a  bottle  a  day,  sir  ! 

Poor  Galileo,  forced  to  rat 

Before  the  Inquisition, 
E  pur  si  muove  was  the  pat 

He  gave  them  in  addition  : 
He  meant,  whate'er  you  think  you  prove, 

The  earth  must  go  its  way,  sirs  ; 
Spite  of  your  teeth  I'll  make  it  move, 

For  I'll  drink  my  bottle  a  day,  sirs  ! 

Great  Newton,  who  was  never  beat 

Whatever  fools  may  think,  sir  ; 
Though  sometimes  he  forgot  to  eat, 

He  never  forgot  to  drink,  sir  : 
Descartes4  took  nought  but  lemonade, 

To  conquer  him  was  play,  sir  ; 
The  first  advance  that  Newton  made 

Was  to  drink  his  bottle  a  day,  sir ! 

1  The  common  epithet  of  rank:  nobilis  Tycho,  as  he  was  a  nobleman.     The  writer 
had  been  at  history. 

2  He   lost   it  in  a  duel,  with  Manderupius  Pasbergius.     A  contemporary,   T.  B. 
Laurus,   insinuates  that  they  fought  to   settle  which  was  the  best  mathematician  ! 
This  seems  odd,  but  it  must  be  remembered  they  fought  in  the  dark,  '  in  tenebris 
densis' ;  and  it  is  a  nice  problem  to  shave  off  a  nose  in  the  dark,  without  any  other 
harm. 

*  Referring  to  Kepler's  celebrated  law  of  planetary  motion.  He  had  previously 
wasted  his  time  on  analogies  between  the  planetary  orbits  and  the  polyhedrons. 

4  As  great  a  lie  as  ever  was  told:  but  in  1800  a  compliment  to  Newton  without  a 
fling  at  Descartes  would  have  been  held  a  lopsided  structure. 


236  A   BUDGET   OF  PARADOXES; 

D'Alemberfc,  Euler,  and  Clairaut, 

Though  they  increased  our  store,  sir, 
Much  further  had  been  seen  to  go 

Had  they  tippled  a  little  more,  sir  ! 
Lagrange  gets  mellow  with  Laplace, 

And  both  are  wont  to  say,  sir, 
The  philosophe  who's  not  an  ass 

Will  drink  his  bottle  a  day,  sir ! 

Astronomers  !    what  can  avail 

Those  who  calumniate  us  ; 
Experiment  can  never  fail 

With  such  an  apparatus  : 
Let  him  who'd  have  his  merits  known 

Remember  what  I  say,  sir ; 
Fair  science  shines  on  him  alone 

Who  drinks  his  bottle  a  day,  sir ! 

How  light  we  reck  of  those  who  mock 

By  this  we'll  make  to  appear,  sir, 
We'll  dine  by  the  sidereal *  clock 

For  one  more  bottle  a  year,  sir  : 
But  choose  which  pendulum  you  will, 

You'll  never  make  your  way,  sir, 
Unless  you  drink — and  drink  your  fill, — 

At  least  a  bottle  a  day,  sir  ! ' 

Old  times  are  changed,  old  manners  gone ! 

There  is  a  new  Mathematical  Society,  and  I  am,  at  this  present 
writing  (1866),  its  first  President.  We  are  very  high  in  the 
newest  developements,  and  bid  fair  to  take  a  place  among  the 
scientific  establishments.  Benjamin  Grompertz,  who  was  President 
of  the  old  Society  when  it  expired,  was  the  link  between  the  old 
and  new  body  :  he  was  a  member  of  ours  at  his  death.  But  not 
a  drop  of  liquor  is  seen  at  our  meetings,  except  a  decanter  of 
water  :  all  our  heavy  is  a  fermentation  of  symbols  ;  and  we  do  not 
draw  it  mild.  There  is  no  penny  fine  for  reticence  or  occult 
science  ;  and  as  to  a  song  !  not  the  ghost  of  a  chance. 

1826.  The  time  may  have  come  when  the  original  documents 
connected  with  the  discovery  of  Neptune  may  be  worth  revising. 
The  following  are  extracts  from  the  Athenceum  of  October  3  and 
October  17  : — 


1  The  sidereal  day  is  about  four  miuutes  short  of  the  solar ;   there  are  366  sidereal 
<3:iys  in  the  year. 


LETTER  FROM  SIR  JOHN  IIERSCIIEL.  237 


LE    VERRIER'S    PLANET. 

"We  have  received,  at  the  last  moment  before  making  up  for 
press,  the  following  letter  from  Sir  John  Herschel,  in  reference 
to  the  matter  referred  to  in  the  communication  from  Mr.  Hind 
given  below  : — 

Collingwood,  Oct.  1. 

'  In  my  address  to  the  British  Association  assembled  at  Southampton, 
on  the  occasion  of  my  resigning  the  chair  to  Sir  R.  Murchison,  I  stated, 
among  the  remarkable  astronomical  events  of  the  last  twelvemonth, 
that  it  had  added  a  new  planet  to  our  list, — adding,  "  it  has  done  more, 
— it  has  given  us  the  probable  prospect  of  the  discovery  of  another. 
We  see  it  as  Columbus  saw  America  from  the  shores  of  Spain.  Its 
movements  have  been  felt,  trembling  along  the  far- reaching  line  of  our 
analysis,  with  a  certainty  hardly  inferior  to  that  of  ocular  demonstra- 
tion."—  These  expressions  are  not  reported  in  any  of  the  papers  which 
profess  to  give  an  account  of  the  proceedings,  but  I  appeal  to  all  pre- 
sent whether  they  were  not  used. 

Give  me  leave  to  state  my  reasons  for  this  confidence ;  and,  in  so 
doing,  to  call  attention  to  some  facts  which  deserve  to  be  put  on  record 
in  the  history  of  this  noble  discovery.  On  July  12,  1842,  the  late 
illustrious  astronomer,  Bessel,  honoured  me  with  a  visit  at  my  present 
residence.  On  the  evening  of  that  day,  conversing  on  the  great  work 
of  the  planetary  reductions  undertaken  by  the  Astronomer  Royal — then 
in  progress,  and  since  published,1 — M.  Bessel  remarked  that  the  mo- 
tions of  Uranus,  as  he  had  satisfied  himself  by  careful  examination  of 
the  recorded  observations,  could  not  be  accounted  for  by  the  pertur- 
bations of  the  known  planets  ;  and  that  the  deviations  far  exceeded  any 
possible  limits  of  error  of  observation.  In  reply  to  the  question, 
Whether  the  deviations  in  question  might  not  be  due  to  the  action 
of  an  unknown  planet  ? — he  stated  that  he  considered  it  highly  pro- 
bable that  such  was  the  case, — being  systematic,  and  such  as  might 
be  produced  by  an  exterior  planet.  I  then  inquired  whether  he  had 
attempted,  from  the  indications  afforded  by  these  perturbations,  to 
discover  the  position  of  the  unknown  body, — in  order  that  "  a  hue  and 
cry  "  might  be  raised  for  it.  From  his  reply,  the  words  of  which  I  do 
not  call  to  mind,  I  collected  that  he  had  not  then  gone  into  that  in- 
quiry ;  but  proposed  to  do  so,  having  now  completed  certain  works 
which  had  occupied  too  much  of  his  time.  And,  accordingly,  in  a 
letter  which  I  received  from  him  after  his  return  to  Konigsberg,  dated 
November  14,  1842,  he  says, — "  In  reference  to  our  conversation  at 
Collingwood,  I  announce  to  you  (melde  ich  Ihnen)  that  Uranus  is  not 
forgotten."  Doubtless,  therefore,  among  his  papers  will  be  found  some 
researches  on  the  subject. 

1  The  expense  of  this  magnificent  work   was  defrayed  by  Government  grants,  ob- 
t  lined,  at  the  instance  of  the  British  Association,  in  1833. 


233  A  BUDGET   OF  PARADOXES. 

The  remarkable  calculations  of  M.  Le  Verrier — which  have  pointed 
oat,  as  now  appears,  nearly  the  true  situation  of  the  new  planet,  by 
resolving  the  inverse  problem  of  the  perturbations — if  uncorroborated 
by  repetition  of  the  numerical  calculations  by  another  hand,  or  by 
independent  investigation  from  another  quarter,  would  hardly  justify 
so  strong  an  assurance  as  that  conveyed  by  my  expressions  above 
alluded  to.  But  it  was  known  to  me,  at  that  time,  (I  will  take  the 
liberty  to  cite  the  Astronomer  Royal  as  my  authority)  that  a  similar 
investigation  had  been  independently  entered  into,  and  a  conclusion  as 
to  the  situation  of  the  new  planet  very  nearly  coincident  with  M.  Le 
Verrier's  arrived  at  (in  entire  ignorance  of  his  conclusions),  by  a  young 
Cambridge  mathematician,  Mr.  Adams  ; — who  will,  I  hope,  pardon  this 
mention  of  his  name  (the  matter  being  one  of  great  historical  moment), 
— and  who  will,  doubtless,  in  his  own  good  time  and  manner,  place  his 
calculations  before  the  public. 

J.  F.  W.  HERSCHEL.' 


Discovery  of  Le  Verrier'' s  Planet. 

Mr.  Hind  announces  to  the  Times  that  be  has  received  a  letter 
from  Dr.  Briinnow,  of  the  Eoyal  Observatory  at  Berlin,  giving  the 
very  important  information  that  Le  Verrier's  planet  was  found  by 
M.  Gralle,  on  the  night  of  September  23.  *  In  announcing  this 
grand  discovery,'  he  says, '  I  think  it  better  to  copy  Dr.  Briinnow's 
letter.' 

Berlin,  Sept.  25. 

'  My  dear  Sir, — M.  Le  Yerrier's  planet  was  discovered  here  the  23rd 
of  September,  by  M.  Galie.  It  is  a  star  of  the  8th  magnitude,  but 
with  a  diameter  of  two  or  three  seconds.  Here  are  its  places  :  — 

h.  m.  s.  R.  A.  Declination. 

Sept.  23,  12    0  14-6  M.T.     328°  19'  16'0"        —13°  24'    8'2" 
Sept.  24,    85440-9M.T.     328°  18'  14-3"        —13°  24' 297" 

The  planet  is  now  retrograde,  its  motion  amounting  daily  to  four 
seconds  of  time. 

Yours  most  respectfully,  BRtTNNOW.' 

'  This  discovery,'  Mr.  Hind  says,  '  may  be  justly  considered  one 
of  the  greatest  triumphs  of  theoretical  Astronomy ; '  and  he  adds, 
in  a  postscript,  that  the  planet  was  observed  at  Mr.  Bishop's 
Observatory,  in  the  Regent's  Park,  on  Wednesday  night,  not- 
withstanding the  moonlight  and  hazy  sky.  '  It  appears  bright,' 
he  says,  '  and  with  a  power  of  320  I  can  see  the  disc.  The 
following  position  is  the  result  of  instrumental  comparisons  with 
33  Aquarii  : — 


THE  DISCOVERY  OF  NEPTUNE.  239 

Sept.  30,  at  8h.  IGm.  21s.  Greenwich  mean  time — 

Right  ascension  of  planet         .         .         21h.  52m.  47'15s. 
South  declination    ,  13°  27'  20".' 


THE   NEW   PLANET. 

Cambridge  Observatory,  Oct.  15. 

The  allusion  made  by  Sir  John  Herschel,  in  his  letter  contained  in 
the  Athenaeum  of  October  3,  to  the  theoretical  researches  of  Mr. 
Adams,  respecting  the  newly-discovered  planet,  has  induced  me  to 
request  that  you  would  make  the  following  communication  public.  It 
is  right  that  I  should  first  say  that  I  have  Mr.  Adams's  permission  to 
make  the  statements  that  follow,  so  far  as  they  relate  to  his  labours. 
I  do  not  propose  to  enter  into  a  detail  of  the  steps  by  which  Mr.  Adams 
was  led,  by  his  spontaneous  and  independent  researches,  to  a  conclusion 
that  a  planet  must  exist  more  distant  than  Uranus.  The  matter  is  of 
too  great  historical  moment  not  to  receive  a  more  formal  record  than 
it  would  be  proper  to  give  it  here.  My  immediate  object  is  to  show, 
while  the  attention  of  the  scientific  public  is  more  particularly  directed 
to  the  subject,  that,  with  respect  to  this  remarkable  discovery,  English 
astronomers  may  lay  claim  to  some  merit. 

Mr.  Adams  formed  the  resolution  of  trying,  by  calculation,  to  account 
for  the  anomalies  in  the  motion  of  Uranus  on  the  hypothesis  of  a  more 
distant  planet,  when  he  was  an  undergraduate  in  this  University,  and 
when  his  exertions  for  the  academical  distinction,  which  he  obtained 
in  January  1843,  left  him  no  time  for  pursuing  the  research.  In  the 
course  of  that  year,  he  arrived  at  an  approximation  to  the  position  of 
the  supposed  planot ;  which,  however,  he  did  not  consider  to  be  worthy 
of  confidence,  on  account  of  his  not  having  employed  a  sufficient  number 
of  observations  of  Uranus.  Accordingly,  he  requested  my  intervention 
to  obtain  for  him  the  early  Greenwich  observations,  then  in  course  of 
reduction ; — which  the  Astronomer  Royal  immediately  supplied,  in  the 
kindest  possible  manner.  This  was  in  February,  1844.  In  September, 
1845,  Mr.  Adams  communicated  to  me  values  which  he  had  obtained 
for  the  heliocentric  longitude,  excentricity  of  orbit,  longitude  of  peri- 
helion, and  mass,  of  an  assumed  exterior  planet, — deduced  entirely 
from  unaccounted-for  perturbations  of  Uranus.  The  same  results, 
somewhat  corrected,  he  communicated,  in  October,  to  the  Astronomer 
Royal.  M.  Le  Verrier,  in  an  investigation  which  was  published  in 
June  of  184(5,  assigned  very  nearly  the  same  heliocentric  longitude  for 
the  probable  position  of  the  planet  as  Mr.  Adams  had  arrived  at,  but 
gave  no  results  respecting  its  mass  and  the  form  of  its  orbit.  The 
coincidence  as  to  position  from  two  entirely  independent  investigations 
naturally  inspired  confidence ;  and  the  Astronomer  Royal  shortly  after 
suggested  the  employing  of  the  Northumberland  telescope  of  this 
Observatory  in  a  systematic  search  after  the  hypothetical  planet ;  re- 
commending, at  the  same  time,  a  definite  plan  of  operations.  I  under- 


240 


A  BUDGET   OF  PARADOXES. 


took  to  make  the  search,  —  and  commenced  observing  on  July  29; 
The  observations  were  directed,  in  the  first  instance,  to  the  part  of  the 
heavens  which  theory  had  pointed  out  as  -the  most  probable  place  of 
the  planet  ;  in  selecting  which  I  was  guided  by  a  paper  drawn  up  for 
me  by  Mr.  Adams.  Not  having  hour  xxi.  of  the  Berlin  star-maps  —  of 
the  publication  of  which  I  was  not  aware  —  I  had  to  proceed  on  the 
principle  of  comparison  of  observations  made  at  intervals.  On  July  30, 
I  went  over  a  zone  9'  broad,  in  such  a  manner  as  to  include  all  stars 
to  the  eleventh  magnitude.  On  August  4,  I  took  a  broader  zone,  — 
and  recorded  a  place  of  the  planet.  My  next  observations  were  on 
August  12  ;  when  I  met  with  a  star  of  the  eighth  magnitude  in  the 
zone  which  T  had  gone  over  on  July  30,  —  and  which  did  not  then 
contain  this  star.  Of  course,  this  was  the  planet  ;  —  the  place  of  which 
was,  thus,  recorded  a  second  time  in  four  days  of  observing.  A  com- 
parison of  the  observations  of  July  30  and  August  12  would,  according 
to  the  principle  of  search  which  I  employed,  have  shown  me  the  planet. 
I  did  not  make  the  comparison  till  after  the  detection  of  it  at  Berlin  — 
partly  because  I  had  an  impression  that  a  much  more  extensive  search 
was  required  to  give  any  probability  of  discovery  —  and  partly  from  the 
press  of  other  occupation.  The  planet,  however,  was  secured,  and  two 
positions  of  it  recorded  six  weeks  earlier  here  than  in  any  other 
observatory,  —  and  in  a  systematic  search  expressly  undertaken  for  that 
purpose.  I  give  now  the  positions  of  the  planet  on  August  4  and 
August  12. 


Greenwich  mean  time. 

m    2<5s 
6m.  25s. 

-?m    2fi« 
3m.  26s. 


AIID-    4 
Aug.    4, 

Am*   12 
Aug.  12, 


/R.A.         21h.  58m.  14'70s. 
^NPD      102°  57'      32'2" 

R'A'         21h.  57m.  26'13s. 
103o  2,        fl.2« 


From  these  places  compared  with  recent  observations  Mr.  Adams 
has  obtained  the  following  results  :  — 


Distance  of  the  planet  from  the  sun 
Inclination  of  the  orbit    .         .         . 
Longitude  of  the  descending  node 
Heliocentric  longitude,  Aug.  4 


30-05 
1°  45' 
309°  43' 
326°  39' 


The  present  distance  from  the  sun  is,  therefore,  thirty  times  the  earth's 
mean  distance  ;  —  which  is  somewhat  less  than  the  theory  had  indicated. 
The  other  elements  of  the  orbit  cannot  be  approximated  to  till  the 
observations  shall  have  been  continued  for  a  longer  period. 

The  part  taken  by  Mr.  Adams  in  the  theoretical  search  after  this 
planet  will,  perhaps,  be  considered  to  justify  the  suggesting  of  a  name.. 
With  his  consent,  I  mention  Oceanus  as  one  which  may  possibly  receive 
the  votes  of  astronomers.  —  I  have  authority  to  state  that  Mr.  Adams's 
investigations  will,  in  a  short  time,  be  published  in  detail. 

J.  CHALLIS.' 


DISCOVERY   OF  NEPTUNE  241 


ASTRONOMICAL  POLICE   REPORT. 

"  An  ill-looking  kind  of  body,  who  declined  to  give  any  name, 
was  brought  before  the  Academy  of  Sciences,  charged  with  having 
assaulted  a  gentleman  of  the  name  of  Uranus  in  the  public 
highway.  The  prosecutor  was  a  youngish  looking  person,  wrapped 
up  in  two  or  three  great  coats ;  and  looked  chillier  than  any- 
thing imaginable,  except  the  prisoner, — whose  teeth  absolutely 
shook,  all  the  time. 

Policeman  Le  Verrier  stated  that  he  saw  the  prosecutor  walking 
along  the  pavement,  —  and  sometimes  turning  sideways,  and 
sometimes  running  up  to  the  railings  and  jerking  about  in  a 
strange  way.  Calculated  that  somebody  must  be  pulling  his 
coat,  or  otherwise  assaulting  him.  It  was  so  dark  that  he  could 
not  see ;  but  thought,  if  he  watched  the  direction  in  which  the 
next  odd  move  was  made,  he  might  find  out  something.  When 
the  time  came,  he  set  Briinnow,  a  constable  in  another  division 
of  the  same  force,  to  watch  where  he  told  him ;  and  Briinnow 
caught  the  prisoner  lurking  about  in  the  very  spot, — trying  to 
look  as  if  he  was  minding  his  own  business.  Had  suspected  for 
a  long  time  that  somebody  was  lurking  about  in  the  neighbour- 
hood. Briinnow  was  then  called,  and  deposed  to  his  catching  the 
prisoner  as  described. 

M.  Arago. — Was  the  prosecutor  sober  ? 

Le  Verrier. — Lord,  yes,  your  worship  ;  no  man  who  had  a  drop 
in  him  ever  looks  so  cold  as  he  did. 

M.  Arago. — Did  you  see  the  assault  ? 

Le  Verrier. — I  can't  say  I  did ;  but  I  told  Briinnow  exactly 
how  he'd  be  crouched  down, — just  as  he  was. 

M.  Arago  (to  Briinnow}. — Did  you  see  the  assault  ? 

Briinnow. — No,  your  worship  ;  but  I  caught  the  prisoner. 

M.  Arago. — How  do  you  know  there  was  any  assault  at  all  ? 

Le  Verrier. — I  reckoned  it  could'nt  be  otherwise,  when  I  saw 
the  prosecutor  making  those  odd  turns  on  the  pavement. 

M.  Arago. — You  reckon  and  you  calculate  I  Why,  you'll  tell 
me,  next,  that  you  policemen  may  sit  at  home  and  find  out  all 
that's  going  on  in  the  streets  by  arithmetic.  Did  you  ever  bring 
a  case  of  this  kind  before  me  till  now  ? 

Le  Verriar. — Why,  you  see,  your  worship,  the  police  are  grow- 
ing cleverer  and  cleverer  every  day.  We  can't  help  it : — it  grows 
upon  us. 

fc 


242  A    BUDGET   OF  PAKADOXES. 

M.  Arago. — You're  getting  too  clever  for  me.  What  does  the 
prosecutor  know  about  the  matter  ? 

The  prosecutor  said,  all  he  knew  was  that  he  was  pulled  behind 
by  somebody  several  times.  On  being  further  examined,  he  said 
that  he  had  seen  the  prisoner  often,  but  did  not  know  his  name, 
nor  how  he  got  his  living;  but  had  understood  he  was  called 
Neptune.  He  himself  had  paid  rates  and  taxes  a  good  many 
years  now.  Had  a  family  of  six, — two  of  whom  got  their  own 
living. 

The  prisoner,  being  called  on  for  his  defence,  said  that  it  was 
a  quarrel.  He  had  pushed  the  prosecutor — and  the  prosecutor 
had  pushed  him.  They  had  known  each  other  a  long  time,  and 
were  always  quarrelling ; — he  did  not  know  why.  It  was  their 
nature,  he  supposed.  He  further  said,  that  the  prosecutor  had 
given  a  false  account  of  himself; — that  he  went  about  under 
different  names.  Sometimes  he  was  called  Uranus,  sometimes 
Herschel,  and  sometimes  Greorgium  Sidus;  and  he  had  no 
character  for  regularity  in  the  neighbourhood.  Indeed,  he  was 
sometimes  not  to  be  seen  for  a  long  time  at  once. 

The  prosecutor,  on  being  asked,  admitted,  after  a  little  hesita- 
tion, that  he  had  pushed  and  pulled  the  prisoner  too.  In  the 
altercation  which  followed,  it  was  found  very  difficult  to  make 
out  which  began  : — and  the  worthy  magistrate  seemed  to  think 
they  must  have  begun  together. 

M.  Arago. — Prisoner,  have  you  any  family  ? 

The  prisoner  declined  answering  that  question  at  present.  He 
said  he  thought  the  police  might  as  well  reckon  it  out  whether 
he  had  or  not. 

M.  Arago  said  he  didn't  much  differ  from  that  opinion. — He 
Jien  addressed  both  prosecutor  and  prisoner ;  and  told  them  that 
if  they  couldn't  settle  their  differences  without  quarrelling  in 
the  streets,  he  should  certainly  commit  them  both  next  time. 
In  the  meantime,  he  called  upon  both  to  enter  into  their  own 
recognizances ;  and  directed  the  police  to  have  an  eye  upon  both, 
— observing  that  the  prisoner  would  be  likely  to  want  it  a  long 
time,  and  the  prosecutor  would  be  not  a  hair  the  worse  for  it." 

This  squib  was  written  by  a  person  who  was  among  the  astrono- 
mers :  and  it  illustrates  the  fact  that  Le  Verrier  had  sole  posses- 
sion of  the  field  until  Mr.  Challis's  letter  appeared.  Sir  John 
Herschel's  previous  communication  should  have  paved  the  way  : 
but  the  wonder  of  the  discovery  drove  it  out  of  many  heads. 
There  is  an  excellent  account  of  the  whole  matter  in  Professor 


THE  MOON  AND  THE   TIDES.  243 

Grant's  '  History  of  Physical  Astronomy.'  The  squib  scandalized 
some  grave  people,  who  wrote  severe  admonitions  to  the  editor. 
There  are  formalists  who  spend  much  time  in  writing  propriety 
to  journals,  to  which  they  serve  as  foolometers.  In  a  letter  to 
the  Athenceum,  speaking  of  the  way  in  which  people  hawk  fine 
terms  for  common  things,  I  said  that  these  people  ought  to  have 
a  new  translation  of  the  Bible,  which  should  contain  the  verse 
*  gentleman  and  lady,  created  He  them.'  The  editor  was  hand- 
somely fired  and  brimstoned ! 

A  new  theory  of  the  tides  :  in  which  the  errors  of  the  usual  theory 
are  demonstrated  ;  and  proof  shewn  that  the  full  moon  is  not 
the  cause  of  a  concomitant  spring  tide,  but  actually  the  cause  of 
the  neaps  .  .  .  By  Commr.  Debenham,  B.N.  London,  1846, 
8vo. 

The  author  replied  to  a  criticism  in  the  Athenceum,  and  I 
remember  how,  in  a  very  few  words,  he  showed  that  he  had 
read  nothing  on  the  subject.  The  reviewer  spoke  of  the  forces  of 
the  planets  (i.e.  the  Sun  and  Moon)  on  the  Ocean,  on  which  the 
author  remarks,  '  But  N.B.  the  Sun  is  no  planet,  Mr.  Critic.' 
Had  he  read  any  of  the  actual  investigations  on  the  usual  theory, 
he  would  have  known  that  to  this  day  the  sun  and  moon  con- 
tinue to  be  called  planets — though  the  phrase  is  disappearing — 
in  speaking  of  the  tides ;  the  sense,  of  course,  being  the  old  one, 
wandering  bodies. 

A  large  class  of  the  paradoxers,  when  they  meet  with  some- 
thing which  taken  in  their  sense  is  absurd,  do  not  take  the 
trouble  to  find  out  the  intended  meaning,  but  walk  off  with  the 
words  laden  with  their  own  first  construction.  Such  men  are 
hardly  fit  to  walk  the  streets  without  an  interpreter.  I  was 
startled  for  a  moment,  at  the  time  when  a  recent  happy — and 
more  recently  happier — marriage  occupied  the  public  thoughts, 
by  seeing  in  a  haberdasher's  window,  in  staring  large  letters,  an 
unpunctuated  sentence  which  read  itself  to  me  as  '  Princess 
Alexandra!  collar  and  cuff!'  It  immediately  occurred  to  me 
that  had  I  been  any  one  of  some  scores  out  of  my  paradoxers, 
I  should,  no  doubt,  have  proceeded  to  raise  the  mob  against 
the  unscrupulous  person  who  dared  to  hint  to  a  young  bride  such 
maleficent — or  at  least  immellificent — conduct  towards  her  new 
lord.  But,  as  it  was,  certain  material  contexts  in  the  shop 
window  suggested  a  less  savage  explanation.  A  paradoxer  should 
not  stop  at  reading  the  advertisements  of  Newton  or  Laplace  :  he 
should  learn  to  look  at  the  stock  of  goods. 


244  A  BUDGET   OF  PAEADOXES. 

I  think  I  must  have  an  eye  for  double  readings,  when  pre- 
sented :  though  I  never  guess  riddles.  On  the  day  on  which  I 
first  walked  into  the  Panizzi  reading  room — as  it  ought  to  be 
called — at  the  Museum,  I  began  my  circuit  of  the  wall-shelves 
at  the  ladies'  end :  and  perfectly  coincided  in  the  propriety  of 
the  Bibles  and  theological  works  being  placed  there.  But  the 
very  first  book  I  looked  on  the  back  of  had,  in  flaming  gold 
letters,  the  following  inscription — '  Blast  the  Antinomians  ! '  If 
a  line  had  been  drawn  below  the  first  word,  Dr.  Blast's  history 
of  the  Antinomians  would  not  have  been  so  fearfully  misinter- 
preted. It  seems  that  neither  the  binder  nor  the  arranger  of  the 
room  had  caught  my  reading.  The  book  was  removed  before  the 
catalogue  of  books  of  reference  was  printed. 

Two  systems  of  astronomy  :  first,  the  Newtonian  system,  showing 
the  rise  and  progress  thereof,  with  a  short  historical  account ; 
the  general  theory  with  a  variety  of  remarks  thereon :  second, 
the  system  in  accordance  with,  the  Holy  Scriptures,  showing 
the  rise  and  progress  from  Enoch,  the  seventh  from  Adam,  the 
prophets,  Moses,  and  others,  in  the  first  Testament ;  our  Lord 
Jesus  Christ,  and  his  apostles,  in  the  new  or  second  Testament ; 
Reeve  and  Muggleton,  in  the  third  and  last  Testament ;  with 
a  variety  of  remarks  thereon.  By  Isaac  Frost.  London,  1846, 
4to. 

A  very  handsomely  printed  volume,  with  beautiful  plates. 
Many  readers  who  have  heard  of  Muggleton ians  have  never  had 
any  distinct  idea  of  Lodowick  Muggleton,  the  inspired  tailor, 
(1608-1698)  who  about  1650  received  his  commission  from 
heaven,  wrote  a  Testament,  founded  a  sect,  and  descended  to 
posterity.  Of  Eeeve  less  is  usually  said  ;  according  to  Mr.  Frost, 
he  and  Muggleton  are  the  two  'witnesses.'  I  shall  content 
myself  with  one  specimen  of  Mr.  Frost's  science : 

"  I  was  once  invited  to  hear  read  over  '  Guthrie  on  Astronomy,'  and 
when  the  reading  was  concluded  I  was  asked  my  opinion  thereon  ; 
when  I  said,  '  Doctor,  it  appears  to  me  that  Sir  I.  Newton  has  only 
given  two  proofs  in  support  of  his  theory  of  the  earth  revolving  round 
the  sun :  all  the  rest  is  assertion  without  any  proofs.' — '  What  are 
they  ? '  inquired  the  Doctor. — '  Well,'  I  said,  '  they  are,  first,  the 
power  of  attraction  to  keep  the  earth  to  the  sun ;  the  second  is  the 
power  of  repulsion,  by  virtue  of  the  centrifugal  motion  of  the  earth  : 
all  the  rest  appears  to  me  assertion  without  proof.'  The  Doctor  con- 
sidered a  short  time,  and  then  said,  '  It  certainly  did  appear  so.'  I 
said,  '  Sir  Isaac  has  certainly  obtained  the  credit  of  completing  the 
system,  but  really  he  has  only  half  done  his  work.' — '  How  is  that,' 


MUGGLETON — GEORGE  FOX.  245 

inquired  my  friend  the  Doctor.  My  reply  was  this:  'You  -will 
observe  his  system  shows  the  earth  traverses  round  the  sun  on  an 
inclined  plane  ;  the  consequence  is,  there  are  four  powers  required  to 
make  his  system  complete  : 

1st.     The  power  of  attraction. 

2ndly.     The  power  of  repulsion. 

3rdly.     The  power  of  ascending  the  inclined  plane. 

4thly.     The  power  of  descending  the  inclined  plane. 

You  will  thus  easily  see  the  four  powers  required,  and  Newton  has 
only  accounted  for  two ;  the  work  is  therefore  only  half  done.'  Upon 
due  reflection  the  Doctor  said,  '  It  certainly  was  necessary  to  have 
these  four  points  cleared  up  before  the  system  could  be  said  to  be 
complete.'  ' 

I  have  no  doubt  that  Mr.  Frost,  and  many  others  on  ray  list, 
have  really  encountered  doctors  who  could  be  puzzled  by  such 
stuff  as  this,  or  nearly  as  bad,  among  the  votaries  of  existing 
systems,  and  have  been  encouraged  thereby  to  print  their  ob- 
jections. But  justice  requires  me  to  say  that  from  the  words 
'  power  of  repulsion  by  virtue  of  the  centrifugal  motion  of  the 
earth,'  Mr.  Frost  may  be  suspected  of  having  something  more 
like  a  notion  of  the  much-mistaken  term  '  centrifugal  force ' 
than  many  paradoxers  of  greater  fame.  The  Muggletonian  sect 
is  not  altogether  friendless :  over  and  above  this  handsome 
volume,  the  works  of  Eeeve  and  Muggleton  were  printed,  in  1832, 
in  three  quarto  volumes.  See  Notes  and  Queries,  1st  Series,  v. 
80  ;  3rd  Series,  iii,  303. 

[The  system  laid  down  by  Mr.  Frost,  though  intended  to  be 
substantially  that  of  Lodowick  Muggleton,  is  not  so  vagari- 
ous. It  is  worthy  of  note  how  very  different  have  been  the 
fates  of  two  contemporary  paradoxers,  Muggleton  and  George 
Fox.  They  were  friends  and  associates,  and  commenced  their 
careers  about  the  same  time,  1647-1650.  The  followers  of  Fox 
have  made  their  sect  an  institution,  and  deserve  to  be  called 
the  pioneers  of  philanthropy.  But  though  there  must  still  be 
Muggletonian s,  since  expensive  books  are  published  by  men  who 
take  the  name,  no  sect  of  that  name  is  known  to  the  world. 
Nevertheless,  Fox  and  Muggleton  are  men  of  one  type,  developed 
by  the  same  circumstances  :  it  is  for  those  who  investigate  such 
men  to  point  out  why  their  teachings  have  had  fates  so  different. 
Macaulay  says  it  was  because  Fox  found  followers  of  more  sense 
than  himself.  True  enough :  but  why  did  Fox  find  such 
followers  and  not  Muggleton  ?  The  two  were  equally  crazy,  to 


246  A  BUDGET   OF  PARADOXES. 

all  appearance :  and  the  difference  required  must  be  sought  in 
the  doctrines  themselves. 

Fox  was  not  a  rational  man  :  but  the  success  of  his  sect  and 
doctrines  entitles  him  to  a  letter  of  alteration  of  the  phrase 
which  I  am  surprised  has  not  become  current.  When  Conduitt, 
the  husband  of  Newton's  half-niece,  wrote  a  circular  to  Newton's 
friends,  just  after  his  death,  inviting  them  to  bear  their  parts  in 
a  proper  biography,  he  said,  '  As  Sir  I.  Newton  was  a  national 
man,  I  think  every  one  ought  to  contribute  to  a  work  intended 
to  do  him  justice.'  Here  is  the  very  phrase  which  is  often 
wanted  to  signify  that  celebrity  which  puts  its  mark,  good  or 
bad,  on  the  national  history,  in  a  manner  which  cannot  be 
asserted  of  many  notorious  or  famous  historical  characters.  Thus 
George  Fox  and  Newton  are  both  national  men.  Dr.  Eoget's 
Thesaurus  gives  more  than  fifty  synonyms — colleagues  would  be 
the  better  word — of  *  celebrated,'  any  one  of  which  might  be 
applied,  either  in  prose  or  poetry,  to  Newton  or  to  his  works,  no 
one  of  which  comes  near  to  the  meaning  which  Conduitt's  ad- 
jective immediately  suggests. 

The  truth  is,  that  we  are  too  monarchical  to  be  national. 
We  have  the  Queen's  army,  the  Queen's  navy,  the  Queen's  high- 
way, the  Queen's  English,  &c. ;  nothing  is  national  except  the 
debt.  That  this  remark  is  not  new  is  an  addition  to  its  force ; 
it  has  hardly  been  repeated  since  it  was  first  made.  It  is  some 
excuse  that  nation  is  not  vernacular  English  :  the  country  is  our 
word,  and  country  man  is  appropriated.] 

Astronomical  Aphorisms,  or  Theory  of  Nature ;  founded  on  the 
immutable  basis  of  Meteoric  Action.  By  P.  Murphy,  Esq. 
London,  1847,  12mo. 

This  is  by  the  framer  of  the  Weather  Almanac,  who  appeals  to 
that  work  as  corroborative  of  his  theory  of  planetary  temperature, 
years  after  all  the  world  knew  by  experience  that  this  meteorolo- 
gical theory  was  just  as  good  as  the  others. 

The  conspiracy  of  the  Bullionists  as  it  affects  the  present  system 
of  the  money  laws.  By  Caleb  Quotem.  Birmingham,  1847, 
8vo.  (pp.  16). 

This  pamphlet  is  one  of  a  class  of  which  I  know  very  little, 
in  which  the  effects  of  the  laws  relating  to  this  or  that  political 
bone  of  contention  are  imputed  to  deliberate  conspiracy  of  one 
class  to  rob  another  of  what  the  one  knew  ought  to  belong  to  the 


THEISM   INDEPENDENT   OF   REVELATION.  247 

other.  The  success  of  such  writers  in  believing  what  they  have 
a  bias  to  believe,  would,  if  they  knew  themselves,  make  them 
think  it  equally  likely  that  the  inculpated  classes  might  really 
believe  what  it  is  their  interest  to  believe.  The  idea  of  a  guilty 
understanding  existing  among  fundholders,  or  landholders,  or 
any  holders,  all  the  country  over,  and  never  detected  except  by 
bouncing  pamphleteers,  is  a  theory  which  should  have  been  left 
for  Cobbett  to  propose,  and  for  Apella  to  believe. 

[August,  1866.  A  pamphlet  shows  how  to  pay  the  National 
Debt.  Advance  paper  to  railways,  &c.,  receivable  in  payment  of 
taxes.  The  railways  pay  interest  and  principal  in  money,  with 
which  you  pay  your  national  debt,  and  redeem  your  notes. 
Twenty-five  years  of  interest  redeems  the  notes,  and  then  the 
principal  pays  the  debt.  Notes  to  be  kept  up  to  value  by  penal- 
ties.] 

The  Reasoner.     No.  45.     Edited  by  G.  J.  Holyoake.     Price  "2d. 
Is  there  sufficient  proof  of  the  existence  of  God  ?     8vo.    1847. 

This  acorn  of  the  holy  oak  was  forwarded  to  me  with  a  manu- 
script note,  signed  by  the  editor,  on  the  part  of  the  '  London 
Society  of  Theological  Utilitarians,'  who  say  '  they  trust  you 
may  be  induced  to  give  this  momentous  subject  your  considera- 
tion.' The  supposition  that  a  middle-aged  person,  known  as  a 
student  of  thought  on  more  subjects  than  one,  had  that  particular 
subject  yet  to  begin,  is  a  specimen  of  what  I  will  call  the  as- 
sumption-trick of  controversy,  a  habit  which  pervades  all  sides 
of  all  subjects.  The  tract  is  a  proof  of  the  good  policy  of  letting 
opinions  find  their  level,  without  any  assistance  from  the  Court 
of  Queen's  Bench.  Twenty  years  earlier  the  thesis  would  have 
been  positive,  '  There  is  sufficient  proof  of  the  non-existence  of 
God,'  and  bitter  in  its  tone.  As  it  stands,  we  have  a  moderate 
and  respectful  treatment — wrong  only  in  making  the  opponent 
argue  absurdly,  as  usually  happens  when  one  side  invents  the 
other — of  a  question  in  which  a  great  many  Christians  have 
agreed  with  the  atheist :  that  question  being — Can  the  existence 
of  God  be  proved  independently  of  revelation?  Many  very 
religious  persons  answer  this  question  in  the  negative,  as  well 
as  Mr.  Holyoake.  And,  this  point  being  settled,  all  who  agree 
in  the  negative  separate  into  those  who  can  endure  scepticism, 
and  those  who  cannot :  the  second  class  find  their  way  to  Chris- 
tianity. This  very  number  of  '  The  Reasoner '  announces  the 
secession  of  one  of  its  correspondents,  and  his  adoption  of  the 
Christian  faith.  This  would  not  have  happened  twenty  years 


248  A  BUDGET  OF  PARADOXES. 

before :  nor,  had  it  happened,  would  it  have  been  respectfully 
announced. 

There  are  people  who  are  very  unfortunate  in  the  expres- 
sion of  their  meaning.  Mr.  Holyoake,  in  the  name  of  the 
4  London  Society,'  &c.,  forwarded  a  pamphlet  on  the  existence 
of  Grod,  and  said  that  the  Society  trusted  I  '  may  be  induced  to 
give '  the  subject  my  '  consideration.'  How  could  I  know  the 
Society  was  one  person,  who  supposed  I  had  arrived  at  a  conclu- 
sion, and  wanted  a  *  guiding  word '  ?  But  so  it  seems  it  was  : 
Mr.  Holyoake,  in  the  English  Leader  of  October  15,  1864,  and  in 
a  private  letter  to  me,  writes  as  follows : — 

"  The  gentleman  who  was  the  author  of  the  argument,  and  who  asked 
me  to  send  it  to  Mr.  De  Morgan,  never  assumed  that  that  gentleman 
had  '  that  particular  subject  to  begin  ' — on  the  contrary,  he  supposed 
that  one  whom  we  all  knew  to  be  eminent  as  a  thinker  had  come  to  a 
conclusion  upon  it,  and  would  perhaps  vouchsafe  a  guiding  word  to 
one  who  was,  as  yet,  seeking  the  solution  of  the  Great  Problem  of 
Theology.  I  told  my  friend  that  '  Mr.  De  Morgan  was  doubtless  pre- 
occupied, and  that  he  must  be  content  to  wait.  On  some  day  of 
courtesy  and  leisure  he  might  have  the  kindness  to  write.'  Nor  was 
I  wrong — the  answer  appears  in  your  pages  at  the  lapse  of  seventeen 
years." 

I  suppose  Mr.  Holyoake's  way  of  putting  his  request  was  the 
stylus  curice  of  the  Society.  A  worthy  Quaker  who  was  sued 
for  debt  in  the  King's  Bench  was  horrified  to  find  himself 
charged  in  the  declaration  with  detaining  his  creditor's  money 
by  force  and  arms,  contrary  to  the  peace  of  our  Lord  the  King, 
&c.  It's  only  the  stylus  curice,  said  a  friend:  I  don't  know 
curice,  said  the  Quaker,  but  he  shouldn't  style  us  peace-breakers. 
The  notion  that  the  nori-existence  of  Grod  can  be  proved,  has 
died  out  under  the  light  of  discussion :  had  the  only  lights 
shone  from  the  pulpit  and  the  prison,  so  great  a  step  would  never 
have  been  made.  The  question  now  is  as  above.  The  dictum 
that  Christianity  is  '  part  and  parcel  of  the  law  of  the  land '  is 
also  abrogated  :  at  the  same  time,  and  the  coincidence  is  not 
an  accident,  it  is  becoming  somewhat  nearer  the  truth  that  the 
law  of  the  land  is  part  and  parcel  of  Christianity.  It  must  also 
be  noticed  that  Christianity  was  part  and  parcel  of  the  articles 
of  war;  and  so  was  duelling.  Any  officer  speaking  against 
religion  was  to  be  cashiered  ;  and  any  officer  receiving  an  affront 
without,  in  the  last  resort,  attempting  to  kill  his  opponent,  was 
also  to  be  cashiered.  Though  somewhat  of  a  book-hunter,  I 
have  never  been  able  to  ascertain  the  date  of  the  collected 


LOST  EPISCOPAL  PBOTEST.  249 

remonstrances  of  the  prelates  in  the  House  of  Lords  against  this 
overt  inculcation  of  murder,  under  the  soft  name  of  satisfaction  : 
it  is  neither  in  Watt,  nor  in  Lowndes,  nor  in  any  edition  of 
Brunet ;  and  there  is  no  copy  in  the  British  Museum.  Was  the 
collected  edition  really  published  ? 

[The  publication  of  the  above  in  the  Athenceum  has  not  pro- 
duced reference  to  a  single  copy.  The  collected  edition  seems 
to  be  doubted.  I  have  even  met  one  or  two  persons  who  doubt 
the  fact  of  the  Bishops  having  remonstrated  at  all :  but  their 
doubt  was  founded  on  an  absurd  supposition,  namely,  that  it  was 
no  business  of  theirs  ;  that  it  was  not  the  business  of  the  prelates 
of  the  Church  in  union  with  the  State  to  remonstrate  against 

O 

the  Crown  commanding  murder !  Some  say  that  the  edition 
was  published,  but  under  an  irrelevant  title,  which  prevented 
people  from  knowing  what  it  was  about.  Such  things  have 
happened :  for  example,  arranged  extracts  from  Wellington's 
general  orders,  which  would  have  attracted  attention,  fell 
dead  under  the  title  of  'Principles  of  War.'  It  is  surmised 
that  the  book  I  am  looking  for  also  contains  the  protests  of 
the  Eeverend  bench  against  other  things  besides  the  Thou-shalt- 
do-murder  of  the  Articles  (of  war),  and  is  called  *  First  Elements 
of  Eeligion '  or  some  similar  title.  Time  clears  up  all  things.] 

With  the  general  run  of  the  philosophical  atheists  of  the  last 
century  the  notion  of  a  God  was  an  hypothesis.  There  was  left 
an  admitted  possibility  that  the  vague  somewhat  which  went  by 
more  names  than  one,  might  be  personal,  intelligent,  and  super- 
intendent. In  the  works  of  Laplace,  who  is  sometimes  called 
an  atheist  from  his  writings,  there  is  nothing  from  which  such 
an  inference  can  be  drawn  :  unless  indeed  a  Eeverend  Fellow  of 
the  Eoyal  Society  may  be  held  to  be  the  fool  who  said  in  his 
heart,  &c.  &c.,  if  his  contributions  to  the  Philosophical  Trans- 
actions go  no  higher  than  nature.  The  following  anecdote  is 
well  known  in  Paris,  but  has  never  been  printed  entire.  Laplace 
once  went  in  form  to  present  some  edition  of  his  { Systeme  dti 
Monde '  to  the  First  Consul,  or  Emperor.  Napoleon,  whom  some 
wags  had  told  that  this  book  contained  no  mention  of  the  name 
of  God,  and  who  was  fond  of  putting  embarrassing  questions, 
received  it  with — '  M.  Laplace,  they  tell  me  you  have  written 
this  large  book  on  the  system  of  the  universe,  and  have  never 
even  mentioned  its  Creator.'  Laplace,  who,  though  the  most 
supple  of  politicians,  was  as  stiff  as  a  martyr  on  every  point  of 


250  A  BUDGET  OF  PARADOXES. 

his  philosophy  or  religion  (ex.  gr.  even  under  Charles  X.  he 
never  concealed  his  dislike  of  the  priests),  drew  himself  up,  and 
answered  bluntly,  '  Je  n'avais  pas  hesoin  de  cette  hypothese-la.' 
Napoleon,  greatly  amused,  told  this  reply  to  Lagrange,  who 
exclaimed,  '  Ah  I  c'est  une  belle  hypothese ;  ca  explique  beaucoup 
de  choses.' 

It  is  commonly  said  that  the  last  words  of  Laplace  were  '  Ce 
que  nous  connaissons  est  peu  de  chose ;  ce  que  nous  ignorons 
est  immense.'  This  looks  like  a  parody  on  Newton's  pebbles  : 
the  following  is  the  true  account ;  it  comes  to  me  through  one 
remove  from  Poisson.  After  the  publication  (in  1825)  of  the 
fifth  volume  of  the  Mecanique  Celeste,  Laplace  became  gradually 
weaker,  and  with  it  musing  and  abstracted.  He  thought  much 
on  the  great  problems  of  existence,  and  often  muttered  to  himself 
Qii}est  ce  que  c'est  que  tout  cela !  After  many  alternations,  he 
appeared  at  last  so  permanently  prostrated  that  his  family  applied 
to  his  favorite  pupil,  M.  Poisson,  to  try  to  get  a  word  from  him. 
Poisson  paid  a  visit,  and  after  a  few  words  of  salutation,  said  '  J'ai 
une  bonne  nouvelle  a  vous  annoncer :  on  a  recu  au  Bureau  des 
Longitudes  une  lettre  d'Allemagne  annoncant  que  M.  Bessel 
a  verifie  par  1'observation  vos  decouvertes  theoriques  sur  les 
satellites  de  Jupiter.'  Laplace  opened  his  eyes  and  answered 
with  deep  gravity, '  L'homme  ne  poursuit  que  des  chimeres.'  He 
never  spoke  again.  His  death  took  place  March  5,  1827. 

The  language  used  by  the  two  great  geometers  illustrates  what 
I  have  said :  a  supreme  and  guiding  intelligence —  apart  from  a 
blind  rule  called  nature  of  things — was  an  hypothesis.  The 
absolute  denial  of  such  a  ruling  power  was  not  in  the  plan  of  the 
higher  philosophers :  it  was  left  for  the  smaller  fry.  A  round 
assertion  of  the  non-existence  of  anything  which  stands  in  the 
way  is  the  refuge  of  a  certain  class  of  minds  :  but  it  succeeds 
only  with  things  subjective  ;  the  objective  offers  resistance.  A 
philosopher  of  the  appropriative  class  tried  it  upon  the  constable 
who  appropriated  him :  I  deny  your  existence,  said  he ;  Come 
along,  all  the  same,  said  the  unpsychological  policeman. 

Euler  was  a  believer  in  Grod,  downright  and  straightforward. 
The  following  story  is  told  by  Thiebault,  in  his  Souvenirs  de 
vingt  ans  de  sejour  a  Berlin,  published  in  his  old  age,  about 
1 804.  This  volume  was  fully  received  as  trustworthy ;  and 
Marshal  Mollendorff  told  the  Due  de  Bassano  in  1 807  that  it  was 
the  most  veracious  of  books  written  by  the  most  honest  of  men. 
Thiebault  says  that  he  has  no  personal  knowledge  of  the  truth  of 
the  story,  but  that  it  was  believed  throughout  the  whole  of  the 


ROTATION   OF  THE   MOON.  251 

north  of  Europe.  Diderot  paid  a  visit  to  the  Eussian  Court  at 
the  invitation  of  the  Empress.  He  conversed  very  freely,  and 
gave  the  younger  members  of  the  Court  circle  a  good  deal  of 
lively  atheism.  The  Empress  was  much  amused,  but  some  of  her 
councillors  suggested  that  it  might  be  desirable  to  check  these 
expositions  of  doctrine.  The  Empress  did  not  like  to  put  a  direct 
muzzle  on  her  guest's  tongue,  so  the  following  plot  was  contrived. 
Diderot  was  informed  that  a  learned  mathematician  was  in  pos- 
session of  an  algebraical  demonstration  of  the  existence  cf  God, 
and  would  give  it  him  before  all  the  Court,  if  he  desired  to  hear 
it.  Diderot  gladly  consented :  though  the  name  of  the  mathe- 
matician is  not  given,  it  was  Euler.  He  advanced  towards 
Diderot,  and  said  gravely,  and  in  a  tone  of  perfect  conviction : 

ft        I       7j  ** 

Monsieur,  — — =  x,  done  Dieu  existe ;  repondez  !   Diderot, 

n 

to  whom  algebra  was  Hebrew,  was  embarrassed  and  disconcerted  5 
while  peals  of  laughter  rose  on  all  sides.  He  asked  permifesion 
to  return  to  France  at  once,  which  was  granted. 

An  examination  of  the  Astronomical  doctrine  of  the  Moon's  rota- 
tion.    By  J.  L.     Edinburgh,  1847,  8vo. 

A  systematic  attack  of  the  character  afterwards  made  with  less 
skill  and  more  notice  by  Mr.  Jellinger  Symons. 

July  1866,  J.  L.  appears  as  Mr.  James  Laurie,  with  a  new 
pamphlet  'The  Astronomical  doctrines  of  the  Moon's  rotation 
.  .  .  .'  Edinburgh.  Of  all  the  works  I  have  seen  on  the  question, 
this  is  the  most  confident,  and  the  sorest.  A  writer  on  astronomy 
said  of  Mr.  Jellinger  Symons,  '  Of  course  he  convinced  no  one  who 
knew  anything  of  the  subject.'  This  '  ungenerous  slur 'on  the 
speculator's  memory  appears  to  have  been  keenly  felt ;  but  its  truth 
is  admitted.  Those  who  knew  anything  of  the  subject  are  '  the 
so-called  men  of  science,'  whose  three  P's  were  assailed ;  prestige, 
pride,  and  prejudice :  this  the  author  tries  to  effect  for  himself 
with  three  Q's ;  quibble,  quirk,  and  quiddity.  He  explains  that 
the  Scribes  and  Pharisees  would  not  hear  Jesus,  and  that  the 
lordly  bishop  of  Eome  will  not  cast  his  tiara  and  keys  at  the  feet 
of  the  '  humble  presbyter '  who  now  plays  the  part  of  pope  in 
Scotland.  I  do  not  know  whom  he  means  :  but  perhaps  the 
friends  of  the  presbyter-pope  may  consider  this  an  ungenerous 
slur.  The  best  proof  of  the  astronomer  is  just  such  '  as  might 
have  been  expected  from  the  merest  of  blockheads ' ;  but  as  the 
giver  is  of  course  not  a  blockhead,  this  circumstance  shows  how 
deeply  blinded  by  prejudice  he  must  be. 


252  A  BUDGET  OF  PARADOXES. 

Of  course  the  paradoxers  do  not  persuade  any  persons  who  know 
their  subjects  :  and  so  these  Scribes  and  Pharisees  reject  the 
Messiah.  We  must  suppose  that  the  makers  of  this  comparison 
are  Christians  :  for  if  they  thought  the  Messiah  an  enthusiast  or 
an  impostor,  they  would  be  absurd  in  comparing  those  who  reject 
what  they  take  for  truth  with  others  who  once  rejected  what  they 
take  for  falsehood.  And  if  Christians,  they  are  both  irreverent 
and  blind  to  all  analogy.  The  Messiah,  with  His  Divine  mission 
proved  by  miracles  which  all  might  see  who  chose  to  look,  is 
degraded  into  a  prototype  of  James  Laurie,  ingeniously  astrono- 
mising  upon  ignorant  geometry  and  false  logic,  and  comparing  to 
blockheads  those  who  expose  his  nonsense.  Their  comparison  is 
as  foolish  as — supposing  them  Christians — it  is  profane  :  but,  like 
errors  in  general,  its  other  end  points  to  truth.  There  were 
Pseudochrists  and  Antichrists ;  and  a  Concordance  would  find  the 
real  forerunners  of  all  the  paradoxers.  But  they  are  not  so  clever 
as  the  old  false  prophets :  there  are  none  of  whom  we  should  be 
inclined  to  say  that,  if  it  were  possible,  they  would  deceive  the 
very  educated.  Not  an  Egyptian  among  them  all  can  make 
uproar  enough  to  collect  four  thousand  men  that  are  murderers-^- 
of  common  sense — to  lead  out  into  the  wilderness.  Nothing,  says 
the  motto  of  this  work,  is  so  difficult  to  destroy  as  the  errors  and 
false  facts  propagated  by  illustrious  men  whose  words  have 
authority.  I  deny  it  altogether.  There  are  things  much  more 
difficult  to  destroy :  it  is  much  more  difficult  to  destroy  the  truths 
and  real  facts  supported  by  such  "men.  And  again,  it  is  much 
more  difficult  to  prevent  men  of  no  authority  from  setting  up 
false  pretensions ;  and  it  is  much  more  difficult  to  destroy  asser- 
tions of  fancy  speculation.  Many  an  error  of  thought  and  learning 
has  fallen  before  a  gradual  growth  of  thoughtful  and  learned 
opposition.  But  such  things  as  the  quadrature  of  the  circle,  &c., 
are  never  put  down.  And  why  ?  Because  thought  can  influence 
thought,  but  thought  cannot  influence  self-conceit :  learning  can 
annihilate  learning  :  but  learning  cannot  annihilate  ignorance. 
A  sword  may  cut  through  an  iron  bar ;  and  the  severed  ends  will 
not  reunite :  let  it  go  through  the  air,  and  the  yielding  substance 
is  whole  again  in  a  moment. 

Miracles  versus  Nature :  being  an  application  of  certain  pro- 
positions in  the  theory  of  chances  to  the  Christian  miracles. 
By  Protimalethes.  Cambridge,  1847,  8vo. 

The  theory,  as  may  be  supposed,  is  carried  further  than  most 
students  of  the  subject  would  hold  defensible. 


THE  PLANET  NEPTUNE-STEAM  BALLOONS.  253 


An  astronomical  Lecture.  By  the  Rev.  R.  Wilson.  Greenock, 
1847,  12mo. 

Against  the  moon's  rotation  on  her  axis. 

[Handed  about  in  the  streets  in  1847 :  I  quote  the  whole  :]  Im- 
portant discovery  in  astronomy,  communicated  to  the  Astrono- 
mer Royal,  December  21st,  1846.  That  the  Sun  revolve  round 
the  Planets  in  25748|  years,  in  consequence  of  the  combined 
attraction  of  the  planets  and  their  satellites,  and  that  the  Earth 
revolve  round  the  Moon  in  18  years  and  228  days.  D.  T. 
GLAZIER  [altered  with  a  pen  into  GLAZION.]  Price  one  penny. 

1847.  In  the  United  Service  Magazine  for  September,  1847, 
Mrs.  Borron,  of  Shrewsbury,  published  some  remarks  tending  to 
impeach  the  fact  that  Neptune,  the  planet  found  by  Galle,  really 
was  the  planet  wljich  Le  Verrier  and  Adams  had  a  right  to  claim. 
This  was  followed  (September  14)  by  two  pages,  separately  circu- 
lated, of  '  Further  Observations  upon  the  Planets  Neptune  and 
Uranus,  with  a  Theory  of  Perturbations ' ;  and  (October  19, 1848) 
by  three  pages  of  'A  Keview  of  M.  Leverrier's  Exposition.' 
Several  persons,  when  the  remarkable  discovery  was  made,  con- 
tended that  the  planet  actually  discovered  was  an  intruder ;  and 
the  future  histories  of  the  discovery  must  contain  some  account  of 
this  little  after-piece.  Tim  Linkinwater's  theory  that  there  is  no 
place  like  London  for  coincidences,  would  have  been  utterly  over- 
thrown in  favour  of  what  they  used  to  call  the  celestial  spaces,  if 
there  had  been  a  planet  which  by  chance  was  put  near  the  place 
assigned  to  Neptune  at  the  time  when  the  discovery  was  made. 

Aerial  Navigation ;  containing  a  description  of  a  proposed  flying 
machine,  on  a  new  principle.  By  Daedalus  Britannicus. 
London,  1847,  8vo. 

In  1842-43  a  Mr.  Henson  had  proposed  what  he  called  an 
aeronaut  steam-engine,  and  a  Bill  was  brought  in  to  incorporate 
an  *  Aerial  Transit  Company.'  The  present  plan  is  altogether 
different,  the  moving  power  being  the  explosion  of  mixed  hydro- 
gen and  air.  Nothing  came  of  it — not  even  a  Bill.  What  the 
final  destiny  of  the  balloon  may  be  no  one  knows :  it  may  reason- 
ably be  suspected  that  difficulties  will  at  last  be  overcome. 
Darwin,  in  his  'Botanic  Garden'  (1781),  has  the  following 
prophecy : — 


254  -A  BUDGET   OF  PARADOXES. 

Soon  shall  thy  arm,  unconquered  Steam  !  afar 
Drag  the  slow  barge,  or  drive  the  rapid  car ; 
Or,  on  wide-waving  wings  expanded,  bear 
The  flying  chariot  through  the  fields  of  air. 

Darwin's  contemporaries,  no  doubt,  smiled  pity  on  the  poor  man. 
It  is  worth  note  that  the  two  true  prophecies  have  been  fulfilled 
in  a  sense  different  from  that  of  the  predictions.  Darwin  was 
thinking  of  the  suggestion  of  Jonathan  Hulls,  when  he  spoke  of 
dragging  the  slow  barge :  it  is  only  very  recently  that  the  steam- 
tug  has  been  employed  on  the  canals.  The  car  was  to  be  driven, 
not  drawn,  and  on  the  common  roads.  Perhaps,  the  flying 
chariot  will  be  something  of  a  character  which  we  cannot  imagine, 
even  with  the  two  prophecies  and  their  fulfilments  to  help  us. 

A  book  for  the  public.  New  Discovery.  The  causes  of  the 
circulation  of  the  blood  ;  and  the  true  nature  of  the  planetary 
system.  London,  1848,  8vo. 

Light  is  the  sustainer  of  motion  both  in  the  earth  and  in  the 
blood.  The  natural  standard,  the  pulse  of  a  person  in  health, 
four  beats  to  one  respiration,  gives  the  natural  second,  which  is 
the  measure  of  the  earth's  progress  in  its  daily  revolution.  The 
Greek  fable  of  the  Titans  is  an  elaborate  exposition  of  the  atomic 
theory  :  but  any  attempt  to  convince  learned  classics  would  only 
meet  their  derision ;  so  much  does  long-fostered  prejudice  stand 
in  the  way  of  truth.  The  author  complains  bitterly  that  men  of 
science  will  not  attend  to  him  and  others  like  him :  he  observes, 
that  '  in  the  time  occupied  in  declining,  a  man  of  science  might 
test  the  merits.'  This  is,  alas !  too  true ;  so  well  do  applicants 
of  this  kind  know  how  to  stick  on.  But  every  rule  has  its 
exception :  I  have  heard  of  one.  The  late  Lord  Spencer — the 
Lord  Althorp  of  the  House  of  Commons — told  me  that  a  speculator 
once  got  access  to  him  at  the  Home  Office,  and  was  proceeding  to 
unfold  his  way  of  serving  the  public.  '  I  do  not  understand  these 

things,'  said  Lord  Althorp,  '  but  I  happen  to  have (naming 

an  eminent  engineer)  upstairs ;  suppose  you  talk  to  him  on  the 
subject.'  The  discoverer  went  up,  and  in  half-an-hour  returned, 
and  said,  '  I  am  very  much  obliged  to  your  Lordship  for  intro- 
ducing me  to  Mr. ;  he  has  convinced  me  that  I  am  quite 

wrong.'  I  supposed,  when  I  heard  the  story — but  it  would  not 
have  been  seemly  to  say  it — that  Lord  A.  exhaled  candour  and 
sense,  which  infected  those  who  came  within  reach  :  he  would 
have  done  so,  if  anybody. 


THE  ANGLE  TRISECTED.  255 


A  method  to  trisect  a  series  of  angles  having  relation  to  each 
other ;  also  another  to  trisect  any  given  angle.  By  James 
Sabben.  1848  (two  quarto  pages). 

'The  consequence  of  years  of  intense  thought':  very  likely, 
and  very  sad. 

1848.  The  following  was  sent  to  me  in  manuscript.  I  give 
the  whole  of  it : — 

'  Quadrature  of  the  Circle. — A  quadrant  is  a  curvilinear  angle  tra- 
versing round  and  at  an  equal  distance  from  a  given  point,  called 
a  centre,  no  two  points  in  the  curve  being  at  the  same  angle,  but 
irreptitiously  graduating  from  90  to  60.  It  is  therefore  a  mean  angle 
of  90  and  60,  which  is  75,  because  it  is  more  than  60,  and  less  than  90, 
approximately  from  60  to  90,  and  from  90  to  60,  with  equal  generation 
in  each  irreptitious  approximation,  therefore  meeting  in  75,  and  which 
is  the  mean  angle  of  the  quadrant. 

Or,  suppose  a  line  drawn  from  a  given  point  at  90,  and  from  the 
same  point  a  line  at  60.  Let  each  of  these  lines  revolve  on  this  point 
toward  each  other  at  an  equal  ratio.  They  will  become  one  line  at  75, 
and  bisect  the  curve,  which  is  one-sixth  of  the  entire  circle.  The 
result,  taking  16  as  a  diameter,  gives  an  area  of  201  '072400,  and  a 
circumference  of  50'2681.  3  •  ] 

The  original  conception,  its  natural  harmdny,  and  the  result,  to  my 
own  mind  is  a  demonstrative  truth,  which  I  presume  it  right  to  make 
known,  though  perhaps  at  the  hazard  of  unpleasant  if  not  uncourteous 
remarks.' 

I  have  added  punctuation :  the  handwriting  and  spelling  are 
those  of  an  educated  person ;  the  word  irreptitious  is  indubitable. 
The  whole  is  a  natural  curiosity. 

The  quadrature  and  exact  area  of  the  circle  demonstrated.     By 

Wm.  Peters.     8vo.  n.  d.  (circa  1848). 

Suggestions  as  to  the  necessity  for  a  revolution  in  philosophy  ;  and 
prospectus  for  the  establishment  of  a  new  quarterly,  to  be  called 
the  Physical  Philosopher  and  Heterodox  Review.  By  Q.  E.  D. 
8vo.  1848. 

These  works  are  by  one  author,  who  also  published,  as  appears 
by  advertisement, 

'Newton  rescued  from  the  precipitancy  of  his  followers  through  a 
century  and  a  half,'  and  '  Dangers  along  a  coast  by  correcting  (as  it  is 
called)  a  ship's  reckoning  by  bearings  of  the  land  at  night  fall,  or  in 
a  fog,  nearly  out  of  print.  Subscriptions  are  requested  for  a  new 
edition.' 


256  A  BUDGET  OF  PAEADOXES. 

The  area  of  a  circle  is  made  four-fifths  of  the  circumscribed 
square :  proved  on  an  assumption  which  it  is  purposed  to  explain 
in  a  longer  essay.  The  author,  as  Q.  E.  D.,  was  in  controversy 
with  the  Athenaeum  journal,  and  criticised  a  correspondent,  D., 
who  wrote  against  a  certain  class  of  discoverers.  He  believed  the 
common  theories  of  hydrostatics  to  be  wrong,  and  one  of  his 
questions  vvas — 

'  Have  you  ever  taken  into  account  anent  gravity  and  gravitation  the 
fact  that  a  five  grain  cube  of  cork  will  of  itself  half  sink  in  the  water, 
whilst  it  will  take  20  grains  of  brass,  which  will  sink  of  itself,  to  pull 
under  the  other  half?  Fit  this  if  you  can,  friend  D.,  to  your  notions 
of  gravity  and  specific  gravity,  as  applied  to  the  construction  of  a 
universal  law  of  gravitation.' 

This  the  Athenceum  published — but  without  some  Italics,  for 
which  the  editor  was  sharply  reproved,  as  a  sufficient  specimen  of 
the  quod  erat  D.  monstrandum  :  on  which  the  author  remarks — 
4  D,— Wherefore  the  e  caret  ?  is  it  D  apostrophe  ?  D',  D'M,  D'Mo, 
D'Monstrandum ;  we  cannot  find  the  wit  of  it.'  This  I  conjecture 
to  contain  an  illusion  to  the  name  of  the  supposed  author ;  but 
whether  De  Mocritus,  De  Mosthenes,  or  De  Moivre  was  intended, 
I  am  not  willing  to  decide. 

The  Scriptural  Calendar  and  Chronological  Reformer,  for  the 
statute  year  1849.  Including  a  review  of  recent  publications 
on  the  Sabbath  question.  London,  1849,  12mo. 

This  is  the  almanac  of  a  sect  of  Christians  who  keep  the  Jewish 
Sabbath,  having  a  chapel  at  Mill  Yard,  Groodman's  Fields.  They 
wrote  controversial  works,  and  perhaps  do  so  still ;  but  I  never 
chanced  to  see  one. 

Geometry  versus  Algebra ;  or  the  trisection  of  an  angle  geometri- 
cally solved.  By  W.  Upton,  B.A.  Bath  (circa  1849).  8vo. 

The  author  published  two  tracts  under  this  title,  containing 
different  alleged  proofs:  but  neither  gives  any  notice  of  the 
change.  Both  contain  the  same  preface,  complaining  of  the 
British  Association  for  refusing  to  examine  the  production.  I 
suppose  that  the  author,  finding  his  first  proof  wrong,  invented 
the  second,  of  which  the  Association  never  had  the  offer ;  and, 
feeling  sure  that  they  would  have  equally  refused  to  examine  the 
second,  thought  it  justifiable  to  present  that  second  as  the  one 
which  they  had  refused.  Mr.  Upton  has  discovered  that  the 
common  way  of  finding  the  circumference  is  wrong,  would  set  it 


TRISECTION   OF   THE   ANGLE.  257 

right  if  he  had  leisure,  and,  in  the  mean  time,  has  solved  the 
problem  of  the  duplication  of  the  cube. 

The  trisector  of  an  angle,  if  he  demand  attention  from  any 
mathematician,  is  bound  to  produce,  from  his  construction,  an 
expression  for  the  sine  or  cosine  of  the  third  part  of  any  angle, 
in  terms  of  the  sine  or  cosine  of  the  angle  itself,  obtained  by  help 
of  no  higher  than  the  square  root.  The  mathematician  knows 
that  such  a  thing  cannot  be ;  but  the  trisector  virtually  says  it 
can  be,  and  is  bound  to  produce  it,  to  save  time.  This  is  the 
misfortune  of  most  of  the  solvers  of  the  celebrated  problems,  that 
they  have  not  knowledge  enough  to  present  those  consequences  of 
their  results  by  which  they  can  be  easily  judged.  Sometimes 
they  have  the  knowledge,  and  quibble  out  of  the  use  of  it.  In 
many  cases  a  person  makes  an  honest  beginning  and  presents  what 
he  is  sure  is  a  solution.  By  conference  with  others  he  at  last  feels 
uneasy,  fears  the  light,  and  puts  self-love  in  the  way  of  it.  Dis- 
honesty sometimes  follows.  The  speculators  are,  as  a  class,  very 
apt  to  imagine  that  the  mathematicians  are  in  fraudulent  con- 
federacy against  them :  I  ought  rather  to  say  that  each  one  of 
them  consents  to  the  mode  in  which  the  rest  are  treated,  and 
fancies  conspiracy  against  himself.  The  mania  of  conspiracy  is  a 
very  curious  subject.  I  do  not  mean  these  remarks  to  apply  to 
the  author  before  me. 

One  of  Mr.  Upton's  trisections,  if  true,  would  prove  the  truth 
of  the  following  equation  : — 

3  cos  |  =   1    +  v/  (4-sin  20) 
o 

which  is  certainly  false. 

In  1852  I  examined  a  terrific  construction,  at  the  request  of 
the  late  Dr.  "Wallich,  who  was  anxious  to  persuade  a  poor  country- 
man of  his  that  trisection  of  the  angle  was  waste  of  time.  One  of 
the  principles  was,  that  '  magnitude  and  direction  determine  each 
other.'  The  construction  was  equivalent  to  the  assertion  that, 
6  being  any  angle,  the  cosine  of  its  third  part  is 

o/j             50    ,       .      o/j      .     50 
sin  30 .  cos h  sin  id  sin  — . 

w  -i 

divided  by  the  square  root  of 

IZ.Q 
sin  230  cos  -  -  +  sin  40  +  sin  30 .  sin  59 .  sin  20 

m 

This  is  from  my  rough  notes,  and  I  believe  it  is  correct.  It 
is  so  nearly  true,  unless  the  angle  be  very  obtuse,  that  common 
drawing,  applied  to  the  construction,  will  not  detect  the  error. 


258  A  BUDGET  OF  PAKADOXES. 

There  are  many  formulae  of  this  kind  :  and  I  have  several  times 
found  a  speculator  who  has  discovered  the  corresponding  con- 
struction, has  seen  the  approximate  success  of  his  drawing — often 
as  great  as  absolute  truth  could  give  in  graphical  practice, — and 
has  then  set  about  his  demonstration,  in  which  he  always  succeeds 
to  his  own  content. 

There  is  a  trisection  of  which  I  have  lost  both  cutting  and 
reference  :  I  think  it  is  in  the  United  Service  Journal.  I  could 
not  detect  any  error  in  it,  though  certain  there  must  be  one. 
At  least  I  discovered  that  two  parts  of  the  diagram  were  incom- 
patible unless  a  certain  point  lay  in  line  with  two  others,  by 
which  the  angle  to  be  trisected — and  which  was  trisected — was 
bound  to  be  either  0°  or  180°. 

Aug.  22,  1866.  Mr.  Upton  sticks  to  his  subject.  He  has  just 
published  '  The  Uptonian  Trisection.  Eespectfully  dedicated  to 
the  schoolmasters  of  the  United  Kingdom.'  It  seems  to  be  a 
new  attempt.  He  takes  no  notice  of  the  sentence  I  have  put  in 
italics :  nor  does  he  mention  my  notice  of  him,  unless  he  mean 
to  include  me  among  those  by  whom  he  has  been  '  ridiculed  and 
sneered  at '  or  '  branded  as  a  brainless  heretic.'  I  did  neither  one 
nor  the  other :  I  thought  Mr.  Upton  a  paradoxer  to  whom  it  was 
likely  to  be  worth  while  to  propound  the  definite  assertion  now 
in  italics  ;  and  Mr.  Upton  does  not  find  it  convenient  to  take 
issue  on  the  point.  He  prefers  general  assertions  about  algebra. 
So  long  as  he  cannot  meet  algebra  on  the  above  question,  he  may 
issue  as  many  '  respectful  challenges '  to  the  mathematicians  as 
he  can  find  paper  to  write :  he  will  meet  with  no  attention. 

There  is  one  trisection  which  is  of  more  importance  than  that 
of  the  angle.  It  is  easy  to  get  half  the  paper  on  which  you 
write  for  margin ;  or  a  quarter  ;  but  very  troublesome  to  get  a 
third.  Show  us  how,  easily  and  certainly,  to  fold  the  paper  into 
three,  and  you  will  be  a  real  benefactor  to  society. 

Early  in  the  century  there  was  a  Turkish  trisector  of  the 
angle,  Hussein  Effendi,  who  published  two  methods.  He  was  the 
father  of  Ameen  Bey,  who  was  well  known  in  England  thirty 
years  ago  as  a  most  amiable  and  cultivated  gentleman  and  an 
excellent  mathematician.  He  was  then  a  student  at  Cambridge  : 

O        " 

and  he  died,  years  ago,  in  command  of  the  army  in  Syria. 
Hussein  Effendi  was  instructed  in  mathematics  by  Ingliz  Selim 
Eifendi,  who  translated  a  work  of  Bonnycastle  into  Turkish. 
This  Englishman  was  Kichard  Baily,  brother  of  Francis  Baily  the 
astronomer,  who  emigrated  to  Turkey  in  his  youth,  and  adopted 


LETTER  FROM  A  CYCLOMETER.  259 

the  manners  of  the  Turks,  but  whether  their  religion  also  I  never 
heard,  though  I  should  suppose  he  did. 

I  now  give  the  letters  from  the  agricultural  labourer  and  his 
friend,  described  in  page  9.  They  are  curiosities ;  and  the 
history  of  the  quadrature  can  never  be  well  written  without  some 
specimens  of  this  kind : — 

'  Doctor  Morgan,  Sir.     Permit  mo  to  address  you 

Brute  Creation  may  perhaps  enjoy  the  faculty  of  behold- 
ing visible  things  with  a  more  penitrating  eye  than  ourselves.  But 
Spiritual  objects  are  as  far  out  of  their  reach  as  though  they  had  no 
being 

Nearest  therefore  to  the  brute  Creation  are  those  men  who  Suppose 
themselves  to  be  so  far  governed  by  external  objects  as  to  believe 
nothing  but  what  they  See  and  feel  And  Can  accomedate  to  their 
Shallow  understanding  and  Imaginations 

My  Dear  Sir  Let  us  all  Consult  ourselves  by  the  wise  proverb.. 

I  believe  that  evry  man*  merit  &  ability  aught  to  be  appreciated 
and  valued  In  proportion  to  its  worth  &  utility 

In  whatever  State  or  Circumstances  they  may  fortunately  or  un- 
fortunately be  placed 

And  happy  it  is  for  evry  man  to  know  his  worth  and  place 

When  a  Gentleman  of  your  Standing  in  Society  Clad  with  those 
honors  Can  not  understand  or  Solve  a  problem  That  is  explicitly  ex- 
plained by  words  and  Letters  and  mathematacally  operated  by  figuers 
He  had  best  consult  the  wise  proverd 

Do  that  which  thou  Canst  understand  and  Comprehend  for  thy 
good. 

I  would  recommend  that  Such  Gentleman  Change  his  business 

And  appropriate  his  time  and  attention  to  a  Sunday  School  to 
Learn  what  he  Could  and  keep  the  Litle  Children  form  durting  their 
Close 

With  Sincere  feelings  of  Gratitude  for  your  weakness  and  Inability 
I  am 

Sir  your  Superior  in  Mathematics ' 

1849  June  th29. 

'  Dor  Morgin  Sir 

I  wrote  and  Sent  my  work  to  Professor of  State  of  • 

United  States 

I  am  now  in  the  possesion  of  the  facts  that  he  highly  approves  of 
my  work.  And  Says  he  will  Insure  me  Reward  in  the  States 

I  write  this  that  you  may  understand  that  I  have  knowledge  of  the 
unfair  way  that  I  am  treated  In  my  own  nati  County 

I  am  told  and  have  reasons  to  believe  that  it  is  the  Clergy  that  treat 
me  so  unjust. 

I  am  not  Desirious  of  heaping  Disonors  upon  my  own  nation.     But 

3  2 


260  A  BUDGET   OF  PARADOXES. 

if  I  have  to  Leave  this  kingdom  without  my  Just  dues.  The  world 
Shall  know  how  I  am  and  have  been  treated. 

I  am  Sir  Desirous  of  my 

Just  dues 

1849  July  3. 

July  7th,  1849. 

Sir,  I  have  been  given  to  understand  that  a  friend  of  mine  one  whom  I 
shall  never  be  ashamed  to  acknowledge  as  such  tho'  lowly  his  origine; 
nay  not  only  not  ashamed  but  proud  of  doing  so  for  I  am  one  of  those 
who  esteem  and  respect  a  man  according  to  his  ability  and  probity, 
deeming  with  Dr.  Watts  '  that  the  mind  is  the  standard  of  the  man,'  has 
laid  before  you  and  asked  your  opinion  of  his  extraordinary  perform- 
ance, viz.  the  quadrature  of  the  circle,  he  did  this  with  the  firmest  belief 
that  you  would  not  only  treat  the  matter  in  a  straightforward  manner 
but  with  the  conviction  that  from  your  known  or  supposed  knowledge 
of  mathematicks  would  have  given  an  upright  and  honorable  decision 
upon  the  subject ;  but  the  question  is  have  you  done  so  ?  Could  I  say 
yes  I  would  with  the  greatest  of  pleasure  and  have  congratulated  you 
upon  your  decision  whatever  it  might  have  been  but  I  am  sorry  to  say 
that  I  cannot  your  letter  is  a  paltry  evasion,  you  say  '  that  it  is  a  great 

pity  that  you  (Mr. )  should  have  attempted  this  (the  quadrature 

of  the  circle)  for  your  mathematical  knowledge  is  not  sufficient  to 
make  you  know  in  what  the  problem  consists,'  you  don't  say  in  what 
it  does  consist  according  to  your  ideas,  oh  !  no  nothing  of  the  sort,  you 
enter  into  no  disquisition  upon  the  subject  in  order  to  show  where  you 

think  Mr.  is  wrong  and  why  you  have  not  is  simply — because 

you  cannot — you  know  that  he  has  done  it  and  what  is  if  I  am  not 
wrongly  informed  you  have  been  heard  to  say  so.  He  has  done  what 
you  nor  any  other  mathematician  as  those  who  call  themselves  such 
have  done.  And  what  is  the  reason  that  you  will  not  candidly  ac- 
knowledge to  him  as  you  have  to  others  that  he  has  squared  the  circle 
shall  I  tell  you  ?  it  is  because  he  has  performed  the  feat  to  obtain  the 
glory  of  which  mathematicians  have  battled  from  time  immemorial 
that  they  might  encircle  their  brows  with  a  wreath  of  laurels  far  more 
glorious  than  ever  conqueror  won  it  is  simply  this  that  it  is  a  poor 
man  a  humble  artisan  who  has  gained  that  victory  that  you  don't  like 
to  acknowledge  it  you  don't  like  to  be  beaten  and  worse  to  acknowledge 
that  you  have  miscalculated,  you  have  in  short  too  small  a  soul  to  ac- 
knowledge that  he  is  right. 

I  was  asked  my  opinion  and  I  gave  it  unhesitatingly  in  the  affirm- 
mative  and  I  am  backed  in  my  opinion  not  only  by  Mr. a  mathe- 
matician and  watchmaker  residing  in  the  boro  of  Southwark  but  by 

no  less  an  authority  than  the  Professor  of  mathematics  of College 

United  States  Mr. and  I  presume  that  he  at  least  is 

your  equal  as  an  authority  and  Mr. says  that  the  government 

of  the  U.  S.  will  recompense  M.  D.  for  the  discovery  he  has  made  if 
so  what  a  reflection  upon  Old  england  the  boasted  land  of  freedom 


THE   MOON'S  KOTATION.  261 

the  nursery  of  the  arts  and  sciences  that  her  sons  are  obliged  to  go  to 
a  foreign  country  to  obtain  that  recompense  to  which  they  are  justly 
entitled 

In  conclusion  I  had  to  contradict  an  assertion  you  made  to  the 
effect  that  '  there  is  not  nor  ever  was  any  reward  offered  by  the 
government  of  this  country  for  the  discovery  of  the  quadrature  of  the 
circle.'  I  beg  to  inform  you  that  there  was  but  that  it  having  been 
deemed  an  impossibility  the  government  has  withdrawn  it,  I  do  this 
upon  no  less  an  authority  than  the  Marquis  of  Northampton. 

I  am,  sir,  yours ' 

Dr.  Morgan. 

Notes  on  the  Kinematic  Effects  of  Revolution  and  Rotation,  with 
reference  to  the  Motions  of  the  Moon  and  of  the  earth.  By 
Henry  Perigal,  Jun.  Esq.  London,  1846-1849,  8vo. 

On  the  misuse  of  technical  terms.  Ambiguity  of  the  terms  Rotation 
and  Revolution,  owing  to  the  double  meaning  improperly  attri- 
buted to  each  of  the  words.  (No  date  nor  place,  but  by  Mr.  Peri- 
gal,  I  have  no  doubt,  and  containing  letters  of  1849  and  1850.) 

The  moon  controversy.  Facts  v.  Definitions.  By  H.  P.,  Jun. 
London,  1856,  8vo.  (pp.  4.) 

Mr.  Henry  Perigal  helped  me  twenty  years  ago  with  the 
diagrams,  direct  from  the  lathe  to  the  wood,  for  the  article 
'  Trochoidal  Curves,'  in  the  Penny  Cyclopaedia  :  these  cuts  add 
very  greatly  to  the  value  of  the  article,  which,  indeed,  could  not 
have  been  made  intelligible  without  them.  He  has  had  many 
years'  experience,  as  an  amateur  turner,  in  combination  of  double 
and  triple  circular  motions,  and  has  published  valuable  diagrams 
in  profusion.  A  person  to  whom  the  double  circular  motion  is 
familiar  in  the  lathe  naturally  looks  upon  one  circle  moving 
upon  another  as  in  simple  motion,  if  the  second  circle  be 
fixed  to  the  revolving  radius,  so  that  one  and  the  same  point 
of  the  moving  circle  travels  upon  the  fixed  circle.  Mr.  Perigal 
commenced  his  attack  upon  the  moon  for  moving  about 
her  axis,  in  the  first  of  the  tracts  above,  ten  years  before 
Mr.  Jellinger  Symons ;  but  he  did  not  think  it  necessary  to 
make  it  a  subject  for  the  Times  newspaper.  His  familiarity 
with  combined  motions  enabled  him  to  handle  his  arguments 
much  better  than  Mr.  J.  Symons  could  do :  in  fact,  he  is  the 
clearest  assailant  of  the  lot  which  turned  out  with  Mr.  J.  Symons. 
But  he  is  as  wrong  as  the  rest.  The  assault  is  now,  I  suppose, 
abandoned,  until  it  becomes  epidemic  again.  This  it  will  do  : 
it  is  one  of  those  fallacies  which  are  very  tempting.  There  was 
a  dispute  on  the  subject  in  1748,  between  James  Ferguson 


262  A   BUDGET  OF  PAEADOXES. 

and  an  anonymous  opponent ;  and  I  think  there  have  been 
others. 

A  poet  appears  in  the  field  (July  19,  1863)  who  calls  himself 
Cyclops,  and  writes  four  octavo  pages.  He  makes  a  distinction 
between  rotation  and  revolution ;  and  his  doctrines  and  phrases 
are  so  like  those  of  Mr.  Perigal  that  he  is  a  follower  at  least. 
One  of  his  arguments  has  so  often  been  used  that  it  is  worth 
while  to  cite  it : — 

Would  Mathematical — forsooth — 
If  true,  have  failed  to  prove  its  truth  ? 
Would  not  they — if  they  could — submit 
Some  overwhelming  proofs  of  it  ? 
But  still  it  totters  proofless  !     Hence 
There's  strong  presumptive  evidence 
None  do — or  can — such  proof  propound 
Because  the  dogma  is  unsound. 
For,  were  there  means  of  doing  so, 
They  would  have  proved  it  long  ago. 

This  is  only  one  of  the  alternatives.  Proof  requires  a  person 
who  can  give  and  a  person  who  can  receive.  I  feel  inspired  to 
add  the  following  : — 

A  blind  man  said,  As  to  the  Sun, 
I'll  take  my  Bible  oath  there's  none  ; 
For  if  tbere  had  been  one  to  show 
They  would  have  shown  it  long  ago. 
How  came  he  such  a  goose  to  be  ? 
Did  he  not  know  he  couldn't  see  ? 
Not  he  ! 

The  absurdity  of  the  verses  is  in  the  argument.  The  writer 
was  not  so  ignorant  or  so  dishonest  as  to  affirm  that  nothing  had 
been  offered  by  the  other  side  as  proof ;  accordingly,  his  syllogism 
amounts  to  this  : — If  your  proposition  were  true,  you  could  have 
given  proof  satisfactory  to  me ;  but  this  you  have  not  done, 
therefore,  your  proposition  is  not  true. 

The  echoes  of  the  moon-controversy  reached  Benares  in 
1857,  in  which  year  was  there  published  a  pamphlet  'Does  the 
Moon  Eotate  ? '  in  Sanscrit  and  English.  The  arguments  are 
much  the  same  as  those  of  the  discussion  at  home. 

We  see  that  there  are  paradoxers  in  argument  as  well  as  in 
assertion  of  fact :  my  plan  does  not  bring  me  much  into  contact 
with  these  ;  but  another  instance  may  be  useful.  Sects,  whether 
religious  or  political,  give  themselves  names  which,  in  meaning, 
are  claimed  also  by  their  opponents ;  loyal,  liberal,  conservative 


3IILNER'S    'END   OF   RELIGIOUS  .CONTROVERSY.'  263 

(of  good),  &c.  have  been  severally  appropriated  by  parties.  Whig 
and  Tory  are  unobjectionable  names :  the  first — which  occurs 
in  English  ballad  as  well  as  in  Scotland — is  sour  milk ;'  the 
second  is  a  robber.  In  theology,  the  Greek  Church  is  Orthodox, 
the  Roman  is  Catholic,  the  modern  Puritan  is  Evangelical,  &c. 

The  word  Christian  (ante,  p.  147)  is  an  instance.  When  words 
begin,  they  carry  their  meanings.  The  Jews,  who  had  their 
Messiah  to  come,  and  the  followers  of  Jesus  of  Nazareth,  who 
took  Him,  for  their  Messiah,  were  both  Christians  (which  means 
Messianites) :  the  Jews  would  never  have  invented  the  term  to 
signify  Jesuans,  nor  would  the  disciples  have  invented  such  an 
ambiguous  term  for  themselves ;  had  they  done  so,  the  Jews 
would  have  disputed  it,  as  they  would  have  done  in  later  times 
if  they  had  had  fair  play.  The  Jews  of  our  day,  I  see  by  their 
newspapers,  speak  of  Jesus  Christ  as  the  Rabbi  Joshua.  But  the 
Heathens,  who  knew  little  or  nothing  about  the  Jewish  hope, 
would  naturally  apply  the  term  Christian  to  the  only  followers 
of  a  Messiah  of  whom  they  had  heard.  For  the  Jesuans  invaded 
them  in  a  missionary  way;  while  the  Jews  did  not  attempt,  at 
least  openly,  to  make  proselytes. 

All  such  words  as  Catholic,  &c.,  are  well  enough  as  mere  nomen- 
clature ;  and  the  world  falls  for  the  most  part,  into  any  names 
which  parties  choose  to  give  themselves.  Silly  people  found  in- 
ferences on  this  concession  ;  and,  as  usually  happens,  they  can 
cite  some  of  their  betters,  St.  Augustine,  a  freakish  arguer,  or, 
to  put  it  in  the  way  of  an  old  writer,  lectorem  ne  multiloquii 
tcedio  fastidiat,  Punicis  quibusdam  argutiis  recreare  solet, 
asks,  with  triumph,  to  what  chapel  a  stranger  would  be  directed, 
if  he  inquired  the  way  to  the  Catholic  assembly  ?  But  the  best 
exhibition  of  this  kind  in  our  own  century  is  that  made  by  the 
excellent  Dr.  John  Milner,  in  a  work  (first  published  in  1801  or 
1802)  which  I  suppose  still  circulates,  'The  End  of  Religious 
Controversy : '  a  startling  title  which,  so  far  as  its  truth  is 
concerned,  might  as  well  have  been  '  The  floor  of  the  bottomless 
pit.'  This  writer,  whom  every  one  of  his  readers  will  swear  to 

1  In  the  old  ballad  of  King  Alfred  and  the  Shepherd,  when  the  latter  is  tempting 
the  disguised  king  into  his  service,  he  says  : 

Of  whig  and  whey  we  have  good  store, 

And  keep  good  pease-straw  fire. 

Whig  is  then  a  preparation  of  milk.  But  another  commonly  cited  derivation  may  be 
suspected  from  the  word  whiggamor  being  used  before  whig,  as  applied  to  the  political 
party ;  whig  may  be  a  contraction.  Perhaps  both  derivations  conspired :  the  word 
whiggamor,  said  to  be  a  word  of  command  to  the  horses,  might  contract  into  whig,  and 
the  contraction  might  br  welcomed  for  its  o\vn  native  meaning. 


264  A  BUDGET   OF  PAEADOXES. 

have  been  a  worthy  soul,  though  many,  even  of  his  own  sect,  will 
not  admire  some  of  his  logic,  speaks  as  follows  : — 

'  Letter  xxv.  On  the  true  Church  being  Catholic.  In  treating 
of  this  third  mark  of  the  true  Church,  as  expressed  in  our  common 
creed,  I  feel  my  spirits  sink  within  me,  and  I  am  almost  tempted 
to  throw  away  my  pen  in  despair.  For  what  chance  is  there  of 
opening  the  eyes  of  candid  Protestants  to  the  other  marks  of  the 
Church,  if  they  are  capable  of  keeping  them  shut  to  this?  Every 
time  they  address  the  Grod  of  Truth,  either  in  solemn  worship  or 
in  private  devotion  [stretch  of  rhetoric],  they  are  forced,  each  of 
them,  to  repeat :  /  believe  in  THE  CATHOLIC  Church,  and  yet  if  I 
ask  any  of  them  the  question  :  Are  you  a  CATHOLIC  ?  he  is  sure 
to  answer  me  No,  I  am  a  PROTESTANT  !  Was  there  ever  a  more 
glaring  instance  of  inconsistency  and  self-condemnation  among 
rational  beings ! ' 

John  Milner,  honest  and  true, 

Did  what  honest  people  still  may  do, 

If  they  write  for  the  many  and  not  for  the  few, 

But  what  by  and  bye  they  must  eschew. 

He  shortened  his  clause;  and  for  a  reason.  If  he  had  used 
the  whole  epithet  which  he  knew  so  well,  any  one  might  have 
given  his  argument  a  half-turn.  Had  he  written,  as  he  ought, 
1  the  Holy  Catholic  Church '  and  then  argued  as  above,  some  sly 
Protestant  would  have  parodied  him  with  '  and  yet  if  I  ask  any 
of  them  the  question  :  Are  you  HOLY  ?  he  is  sure  to  answer  me 
No,  I  am  a  SINNER.'  To  take  the  adjective  from  the  Church,  and 
apply  it  to  the  individual  partisan,  is  recognised  slipslop,  but  not 
ground  of  argument.  If  Dr.  M.  had  asked  his  Protestant  whether 
he  belonged  to  the  Catholic  Church,  the  answer  would  have  been 
Yes,  but  not  to  the  Roman  branch.  When  he  put  his  question 
as  he  did,  he  was  rightly  answered  and  in  his  own  division.  This 
leaving  out  words  is  a  common  practice,  especially  when  the 
emitter  is  in  authority,  and  cannot  be  exposed.  A  year  or  two 
ago  a  bishop  wrote  a  snubbing  letter  to  a  poor  parson,  who  had 
complained  that  he  was  obliged,  in  burial,  to  send  the  worst  of 
sinners  to  everlasting  happiness.  The  bishop  sternly  said  '  hope  l 

1  It  will  be  said  that  when  the  final  happiness  is  spoken  of  in  '  sure  and  certain 
hope,'  it  is  the  Kesurrection,  generally  ;  but  when  afterwards  application  is  made  to 
the  individual,  simple  '  hope'  is  all  that  is  predicated  which  merely  means  '  wish  ? '  I 
know  it :  but  just  before  the  general  declaration,  it  is  declared  that  it  has  pleased  God 
of  his  great  mercy  to  take  unto  Himself,  the  soul  of  our  dear  brother :  and  between 
the  '  hopes '  hearty  thanks  are  given  that  it  has  pleased  God  to  deliver  our  dear 
Iro'.her  out  of  the  miseries  of  this  wicked  world,  with  an  additional  prayer  that  the 
number  of  the  elect  may  shortly  be  accomplished.  All  which  means,  that  our  dear 


THE  BURIAL  SERVICE.  2G5 

is  not  assurance.''  Could  the  clergyman  have  dared  to  answer,  lie 
would  have  said,  '  No,  my  Lord !  but  "  sure  and  certain  hope  "  is 
as  like  assurance  as  a  minikin  man  is  like  a  dwarf.'  Sad  to  say, 
a  theologian  must  be  illogical :  I  fell  sure  that  if  you  took  the 
clearest  headed  writer  on  logic  that  ever  lived,  and  made  a  bishop 
of  him,  he  would  be  shamed  by  his  own  books  in  a  twelvemonth. 

Milner's  sophism  is  glaring  :  but  why  should  Dr.  Milner  be 
wiser  than  St.  Augustine,  one  of  his  teachers  ?  I  am  tempted  to 
let  out  the  true  derivation  of  the  word  Catholic,  as  exclusively 
applied  to  the  Church  of  Rome.  All  can  find  it  who  have  access 
to  the  Rituale  of  Bonaventura  Piscator  (lib.  i.  c.  12,  de  nomine 
Sacrw  Ecclesice,  p.  87  of  the  Venice  folio  of  1537).  I  am  told 
that  there  is  a  Rituale  in  the  Index  Expurgatorius,  but  I  have 
not  thought  it  worth  while  to  examine  whether  this  be  the  one  : 
I  am  rather  inclined  to  think,  as  I  have  heard  elsewhere,  that  the 
book  was  held  too  dangerous  for  the  faithful  to  know  of  it,  even 
by  a  prohibition  :  it  would  not  surprise  me  at  all  if  Roman 
Christians  should  deny  its  existence.1 

It  amuses  me  to  give,  at  a  great  distance  of  time,  a  small 
Eowland  for  a  small  Oliver,  which  I  received,  de  par  VEglise,  so 
far  as  lay  in  the  Oliver-carrier  more  than  twenty  years  ago.  The 
following  contribution  of  mine  to  Notes  and  Queries  (3rd  Ser.  vi. 

brother  is  declared  to  be  taken  to  God,  to  be  in  a  place  not  so  miserable  as  this  world 
— a  description  -which  excludes  the  '  wicked  place  ' — and  to  be  of  the  elect.  Yes,  but 
it  will  be  said  again  !  do  you  not  know  that  when  this  Liturgy  was  framed,  all  who 
were  not  in  the  road  to  Heaven  were  excommunicated,  and  could  not  have  the  burial 
service  read  over  them.  Supposing  the  fact  to  have  been  true  in  old  time,  which  is  a 
very  spicy  supposition,  how  does  that  excuse  the  present  practice?  Have  you  a  right 
always  to  say  what  yon  believe  cannot  always  be  true,  because  you  think  it  was  once 
always  true?  Yes,  but,  choose  whom  you  please,  you  cannot  be  certain  He  is  not 
gone  to  Heaven.  True,  and  choose  which  Bishop  you  please,  you  cannot  be  demon- 
stratively certain,  he  is  not  a  concealed  unbeliever :  may  I  therefore  say  of  the 
whole  bench,  singulatim  et  seriatim,  that  they  are  unbelievers  ?  No  !  No  !  The  voice 
of  common  sense,  of  which  common  logic  is  a  part,  is  slowly  opening  the  eyes  of  the 
multitude  to  the  unprincipled  reasoning  of  theologians.  Remember  1819.  What 
chance  had  Parliamentary  Reform  when  the  House  of  Commons  thanked  the  Man- 
chester sabre-men  ?  If  you  dp  not  reform  your  Liturgy,  it  will  be  reformed  for  yon, 
and  sooner  than  you  think!  The  dishonest  interpretations,  by  defence  of  which  even 
the  minds  of  children  are  corrupted,  and  which  throw  their  shoots  into  literature  and 
commerce,  will  be  sent  to  the  place  whence  they  came :  and  over  the  dcor  of  the 
established  organization  for  teaching  religion  will  be  posted  the  following  notice : — 

Shift  and  Subterfuge,  Shuffle  and  Dodge, 

No  longer  here  allowed  to  lodge  ! 

All  this  ought  to  be  written  by  some  one  who  belongs  to  the  Establishment:  in  him, 
it  would  be  quite  prudent  and  proper;  in  me,  it  is  kind  and  charitable. 

1  This  derivation  lias  been  omitted  (ED.). 


266  A   BUDGET   OF  PAEADOXES. 

p.  175,  Aug.  27,  1864)  will  explain  what  I  say.  There  had  been 
a  complaint  that  a  contributor  had  used  the  term  Papist,  which 
a  very  excellent  dignitary  of  the  Papal  system  pronounced  an 
offensive  term : — 

PAPIST. 

The  term  papist  should  be  stripped  of  all  except  its  etymo- 
logical meaning,  and  applied  to  those  who  give  the  higher  and 
final  authority  to  the  declaration  ex  cathedra  of  the  Pope. 
See  Dr.  Wiseman's  article,  Catholic  Church,  in  the  Penny  Cyclo- 
paedia. 

What  is  one  to  do  about  these  names  ?  First,  it  is  clear  that 
offence  should,  when  possible,  be  avoided :  secondly,  no  one  must 
be  required  to  give  a  name  which  favours  any  assumption  made 
by  those  to  whom  it  is  given,  and  not  granted  by  those  who  give 
it.  Thus  the  subdivision  which  calls  itself  distinctively  Evan- 
gelical has  no  right  to  expect  others  to  concede  the  title.  Now 
the  word  Catholic,  of  course,  falls  under  this  rule ;  and  even 
Roman  Catholic  may  be  refused  to  those  who  would  restrict  the 
word  Catholic  to  themselves.  Roman  Christian  is  unobjec- 
tionable, since  the  Roman  Church  does  not  deny  the  name  of 
Christian  to  those  whom  she  calls  heretics.  No  one  is  bound  in 
this  matter  by  Acts  of  Parliament.  In  many  cases,  no  doubt, 
names  which  have  offensive  association  are  used  merely  by  habit, 
sometimes  by  hereditary  transmission.  Boswell  records  of 
Johnson  that  he  always  used  the  words  'dissenting  teacher,' 
refusing  minister  and  clergyman  to  all  but  the  recipients  of 
episcopal  ordination. 

This  distinctive  phrase  has  been  widely  adopted :  it  occurs 
in  the  Index  of  3rd  S.  iv.  [Notes  and  Queries'].  Here  we  find 
'Platts  (Rev.  John),  Unitarian  teacher,  412;'  the  article  indexed 
has  '  Unitarian  minister.' 

This,  of  course  is  habit :  an  intentional  refusal  of  the  word 
minister  would  never  occur  in  an  index.  I  remember  that,  when 
I  first  read  about  Sam  Johnson's  little  bit  of  exclusiveness,  I  said 
to  myself :  '  Teacher  ?  Teacher  ?  surely  I  remember  One  who  is 
often  called  teacher,  but  never  minister  or  clergyman :  have  not 
the  dissenters  got  the  best  of  it  ? 

When  I  said  that  the  Roman  Church  concedes  the  epithet 
Christians  to  Protestants,  I  did  not  mean  that  all  its  adherents 
do  the  same.  There  is,  or  was,  a  Roman  newspaper,  the  Tablet, 
which,  seven  or  eight  years  ago,  was  one  of  the  most  virulent  of 
the  party  journals.  In  it  I  read,  referring  to  some  complaint  of 


EELIGIOUS   NOMENCLATIVE.— FIDES.  267 

grievance  about  mixed  marriages,  that  if  Christians  would  marry 
Protestants  they  must  take  the  consequences.  My  memory  notes 
this  well ;  because  I  recollected,  when  T  saw  it,  that  there  was  in 
the  stable  a  horse  fit  to  run  in  the  curricle  with  this  one.  About 
seventeen  years  ago  an  Oxford  M.A.,  who  hated  mathematics  like 
a  genuine  Oxonian  of  the  last  century,  was  writing  on  education, 
and  was  compelled  to  give  some  countenance  to  the  nasty  subject. 
He  got  out  cleverly ;  for  he  gave  as  his  reason  for  the  permission, 
that  man  is  an  arithmetical,  geometrical,  and  mechanical  animal, 
as  well  as  a  rational  soul. 

The  Tablet  was  founded  by  an  old  pupil  of  mine,  Mr.  Frederic 
Lucas  ;  who  availed  himself  of  his  knowledge  of  me  to  write  some 
severe  articles — even  abusive,  I  was  told,  but  I  never  saw  them — 
against  me,  for  contributing  to  the  Dublin  Review,  and  poking 
my  heretic  nose  into  orthodox  places.  Dr.  Wiseman,  the  editor, 
came  in  for  his  share,  and  ought  to  have  got  all.  Who  ever 
blamed  the  pig  for  intruding  himself  into  the  cabin  when  the 
door  was  left  open  ?  When  Mr.  Lucas  was  my  pupil,  he  was  of 
the  Society  of  Friends — in  any  article  but  this  I  should  say 
Quaker — and  was  quiet  and  gentlemanly,  as  members  of  that 
Church — in  any  article  but  this  I  should,  from  mere  habit,  say  sect 
— usually  are.  This  is  due  to  his  memory  ;  for,  by  all  I  heard, 
when  he  changed  his  religion  he  ceased  to  be  Lucas  couchant, 
and  became  Lucas  rampant,  fanged  and  langued  gules.  (I  looked 
into  Guillim  to  see  if  my  terms  were  right :  I  could  not  find 
them ;  but  to  prove  I  have  been  there,  I  notice  that  he  calls  a 
violin  a  violent.  How  comes  the  word  to  take  this  form  ?)  I 
met  with  several  Eoman  Christians,  born  and  bred,  who  were  very 
much  annoyed  at  Mr.  Lucas  and  his  doings ;  and  said  some  severe 
things  about  new  converts  needing  kicking-straps. 

The  mention  of  Dr.  Wiseman  reminds  me  of  another  word, 
appropriated  by  Christians  to  themselves :  fides ;  the  Koman  faith 
is  fides,  and  nothing  else  ;  and  the  adherents  vtefiddtB.  Hereby 
hangs  a  retort.  When  Dr.  Wiseman  was  first  in  England,  he 
gave  a  course  of  lectures  in  defence  of  his  creed,  which  were 
thought  very  convincing  by  those  who  were  already  convinced. 
They  determined  to  give  him  a  medal,  and  there  was  a  very 
serious  discussion  about  the  legend.  Dr.  Wiseman  told  me 
himself  that  he  had  answered  to  his  subscribers  that  he  would  not 
have  the  medal  at  all  unless — (naming  some  Italian  authority, 
whom  I  forget)  approved  of  the  legend.  At  last  pro  fide  vindi- 
cata  was  chosen  :  this  may  be  read  either  in  a  Popish  or  heretical 


268  A  BUDGET  OF  PARADOXES. 

sense.  The  feminine  substantive  fides  means  confidence,  trust,  (it 
is  made  to  mean  belief},  but  fidis,  with  the  same  ablative,  fide, 
and  also  feminine,  is  a  fiddle-string.1  If  a  Latin  writer  had  had 
to  make  a  legend  signifying  '  For  the  defence  of  the  fiddle-string,' 
he  could  not  have  done  it  otherwise,  in  the  terseness  of  a  legend, 
than  by  writing  pro  fide  mndicata.  Accordingly,  when  a  Eoman 
Christian  talks  to  you  of  the  faith,  as  a  thing  which  is  his  and 
not  yours,  you  may  say  fiddle.  I  have  searched  Bonaventura 
Piscator  in  vain  for  notice  of  this  ambiguity.  But  the  Greeks 
said  fiddle ;  according  to  Suidas,  cricivSaTra-os — a  word  meaning  a 
four  stringed  instrument  played  with  a  quill — was  an  exclamation 
of  contemptuous  dissent.  How  the  wits  of  different  races  jump  I 

I  am  reminded  of  a  case  of  fides  vindicata,  which,  being  in  a 
public  letter,  responding  to  a  public  invitation,  was  not  meant  to 
be  confidential.  Some  of  the  pupils  of  University  College,  in 
which  all  subdivisions  of  religion  are  (1866;  were,  1867)  on  a 
level,  have  of  course  changed  their  views  in  after  life,  and  become 
adherents  of  various  high  churches.  On  the  occasion  of  a  dinner 
of  old  students  of  the  College,  convened  by  circular,  one  of  these 
students,  whether  then  Eoman  or  Tractarian  Christian  I  do  not 
remember,  not  content  with  simply  giving  negative  answer,  or 
none  at  all,  concocted  a  jorum  of  theological  rebuke,  and  sent  it 
to  the  Dinner  Committee.  Heyday !  said  one  of  them,  this  man 
got  out  of  bed  backwards  !  How  is  that,  said  the  rest  ?  Why,  read 
his  name  backwards,  and  you  will  see.  As  thus  read  it  was — 
No  grub  \ 

To  return  to  Notes  and  Queries.  The  substitution  in  the 
(editorial)  index  of  '  Unitarian  teacher,'  for  the  contributor's 
'  Unitarian  minister,'  struck  me  very  much.  I  have  seldom 
found  such  things  unmeaning.  But  as  the  journal  had  always 
been  free  from  editorial  sectarianisms, — and  very  apt  to  check 
the  contributor! al, — I  could  not  be  sure  in  this  case.  True  it 
was,  that  the  editor  and  publisher  had  been  changed  more  than 
a  year  before  ;  but  this  was  not  of  much  force.  Though  one 
swallow  does  not  make  a  summer,  I  have  generally  found  it 
show  that  summer  is  coming.  However,  thought  I  to  myself, 
if  this  be  Little  Shibboleth,  we  shall  have  Big  Shibboleth  by-and- 
bye.  At  last  it  came.  About  a  twelvemonth  afterwards,  (3rd  S. 
vii.  p.  36)  the  following  was  the  editorial  answer  to  the  question 

1  The  words  are  of  the  same  root,  and  hence  our  word  fiddle.  Some  suppose  this 
root  means  a  rope,  which,  as  that  to  which  you  trust,  becomes,  in  one  divergence, 
confidence  itself —just  as  rock,  and  other  words,  come  to  moan  reliance — and  .in 
another,  a  little  string. 


THE  WORD   CHURCH.  269 

when  the  establishment  was  first  called  the  '  Church  of  England 
and  Ireland  : ' — 

'  That  unmeaning  clause,  "  The  United  Church  of  England  and 
Ireland,"  which  occurs  on  the  title-page  of  The  Book  of  Common  Pratjer, 
was  first  used  at  the  commencement  of  the  present  century.  The 
authority  for  this  phrase  is  the  fifth  article  of  the  Union  of  1800  : 
"  That  the  Churches  of  England  and  Ireland  be  united  into  one 
Protestant  (!)  episcopal  Church,  to  be  called '  The  United  Church,  of 
England  and  Ireland.'  '  Of  course,  churchmen  are  not  responsible 
for  the  theology  of  Acts  of  Parliament,  especially  those  passed  during 
the  dark  ages  of  the  Georgian  era.' 

That  is  to  say,  the  journal  gives  its  adhesion  to  the  party  which 
— under  the  assumed  title  of  the  Church  of  England — claims 
for  the  endowed  corporation  for  the  support  of  religion  rights 
which  Parliament  cannot  control,  and  makes  it,  in  fact,  a  power 
above  the  State.  The  State  has  given  an  inch :  it  calls  this 
corporation  by  the  name  of  the  '  United  Church  of  England  and 
Ireland,'  as  if  neither  England  nor  Ireland  had  any  other  Church. 
The  corporation,  accordingly  aspires  to  an  ell.  But  this  the 
nation  will  only  give  with  the  aspiration  prefixed.  To  illustrate 
my  allusion  in  a  delicate  way  to  polite  ears,  I  will  relate  what 
happened  in  a  Johnian  lecture-room  at  Cambridge,  some  fifty 
years  ago,  my  informant  being  present.  A  youth  of  undue 
aspirations  was  giving  a  proposition,  and  at  last  said,  '  Let  E  F 

be  produced  to  'L  : '  Not  quite  so  far,  Mr. ,  said  the  lecturer, 

quietly,  to  the  great  amusement  of  the  class,  and  the  utter 
astonishment  of  the  aspirant,  who  knew  no  more  than  a  Tract- 
arian  the  tendency  of  his  construction. 

This  word  Church  is  made  to  have  a  very  mystical  meaning. 
The  following  dialogue  between  Ecclesiastes  and  HaBreticus, 
which  I  cannot  vouch  for,  has  often  taken  place  in  spirit,  if  not 
in  letter : — E.  The  word  Church  (sKK\t]aui)  is  never  used  in  the 
New  Testament  except  generally  or  locally  for  that  holy  and 
mystical  body  to  which  the  sacraments  and  the  ordinances  of 
Christianity  are  entrusted.  H.  Indeed !  E.  It  is  beyond  a 
doubt  (here  he  quoted  half  a  dozen  texts  in  support).  H.  Do 
you  mean  that  any  doctrine  or  ordinance  which  was  solemnly 
practised  by  the  £K<\r)(ria  is  binding  upon  you  and  me  ?  E. 
Certainly,  unless  we  would  be  cut  ofi  from  the  congregation  of 
the  faithful.  H.  Have  you  a  couple  of  hours  to  spare  ?  E. 
What  for  ?  H.  If  you  have,  I  propose  we  spend  them  in  cry- 
ing, Great  is  Diana  of  the  Ephesians !  E.  What  do  you  mean  ? 
H.  You  ought  to  know  the  solemn  service  of  the 


270  A  BUDGET   OF  PARADOXES. 

(Acts  xix.  32,  41),  at  Ephesus  ;  which  any  one  might  take  to 
be  true  Church,  by  the  more  part  not  knowing  wherefore  they 
were  come  together,  and  which  was  dismissed,  after  one  of  the 
most  sensible  sermons  ever  preached,  by  the  Eecorder.  E.  I  see 
your  meaning  :  it  is  true,  there  is  that  one  exception  !  H.  Why, 
the  Recorder's  sermon  itself  contains  another,  the  swc^os 
£KK\.r)on,a,  legislative  assembly.  E.  Ah !  the  New  Testament 
can  only  be  interpreted  by  the  Church  I  H.  I  see* !  the  Church 
interprets  itself  into  existence  out  of  the  New  Testament,  and 
then  interprets  the  New  Testament  out  of  existence  into 
itself! 

I  look  upon  all  the  Churches  as  fair  game  which  declare  of 
me  that  absque  dubio  in  wternum  peribo ;  not  for  their  presump- 
tion towards  God,  but  for  their  personal  insolence  towards  myself. 
I  find  that  their  sectaries  stare  when  I  say  this.  Why !  they  do 
not  speak  of  you  in  particular !  These  poor  reasoners  seem  to 
think  that  there  could  be  no  meaning,  as  against  me,  unless  it 
should  be  propounded  that  '  without  doubt  he  shall  perish  ever- 
lastingly, especially  A.  De  Morgan.'  But  I  hold,  with  the  school- 
men, that  '  Omuls  homo  est  animal'  in  conjunction  with  '  Sortes 
est  homo  '  amounts  to  '  Sortes  est  animal.'  But  they  do  not 
mean  it  personally  !  Every  universal  proposition  is  personal  to 
every  instance  of  the  subject.  If  this  be  not  conceded,  then  I 
retort,  in  their  own  sense  and  manner,  '  Whosoever  would  serve 
God,  before  all  things  he  must  not  pronounce  God's  decision 
upon  his  neighbour.  Which  decision,  except  everyone  leave  to 
God  himself,  without  doubt  he  is  a  bigoted  noodle.' 

The  reasoning  habit  of  the  educated  community,  in  four  cases 
out  of  five,  permits  universal  propositions  to  be  stated  at  one 
time,  and  denied,  pro  re  nata,  at  another.  '  Before  we  proceed 
to  consider  any  question  involving  physical  principles,  we  should 
set  out  with  clear  ideas  of  the  naturally  possible  and  impossible.' 
The  eminent  man  who  said  this,  when  wanting  it  for  his  views 
of  mental  education  ( ! )  never  meant  it  for  more  than  what  was 
in  hand,  never  assumed  it  in  the  researches  which  will  give  him 
to  posterity  !  I  have  heard  half-a-dozen  defences  of  his  having 
said  this,  not  one  of  which  affirmed  the  truth  of  what  was  said. 
A  worthy  clergyman  wrote  that  if  A.  B.  had  said  a  certain  thing 
the  point  in  question  would  have  been  established.  It  was  shown 
to  him  that  A.B.  had  said  it,  to  which  the  reply  was  a  refusal 
to  admit  the  point  because  A.  B.  said  it  in  a  second  pamphlet 
and  in  answer  to  objections.  And  I  might  give  fifty  such  instances 
with  very  little  search.  Always  assume  more  than  you  want ; 


PROTESTANT  AND  PAPAL  CHRISTENDOM.         271 

because  you  cannot  tell  how  much  you  may  want  :  put  what  is 
over  into  the  didn't-mean-that  basket,  or  the  extreme  case 
what-not. 

Something  near  forty  years  of  examination  of  the  theologies 
on   and  off — more    years  very   much    on    than    quite   off — have 
given  me  a  good  title — to  myself,  I  ask  no  one  else  for  leave — 
to   make   the  following  remarks  :    A    conclusion  has  premises, 
facts  or  doctrines  from  proof  or  authority,  and  mode  of  inference. 
There  may  be  invention  or  falsehood  of  premise,  with  good  logic  ; 
and  there  may  be  tenable  premise,   followed  by  bad  logic  ;  and 
there  may  be  both  .false  premise  and  bad  logic.     The  Eoman 
system  has  such  a  powerful  manufactory  of  premises,  that  bad 
logic  is  little  wanted  ;  there  is  comparatively  little  of  it.     The 
doctrine-forge  of  the  Eoman  Church  is  one  glorious  compound 
of  everything  that  could  make  Heraclitus  sob  and  Democritus 
snigger.     But  not  the  only  one.      The  Protestants,  in  tearing 
away  from  the  Church  of  Rome,  took  with  them  a  fair  quantity 
of  the  results  of  the  Roman  forge,  which   they  could   not  bring 
themselves  to  give  up.     They  had  more  in  them  of  Martin  than 
of  Jack.     But  they  would  have  no  premises,  except  from  the  New 
Testament ;  though  some  eked  out  with  a  few  general  Councils. 
The  consequence  is  that  they  have  been  obliged  to  find  such  a 
logic   as  would  bring  the  conclusions  they  require  out  of  the 
canonical  books.  And  a  queer  logic  it  is  ;  nothing  but  the  Eoman 
forge  can  be  compared  with  the  Protestant  loom.     The  picking, 
the  patching,  the  piecing,  which  goes  to  the  Protestant  termini 
ad  quem,  would  be  as  remarkable  to  the  general  eye,  as  the 
Eoman   manufacture  of  termini  a  quo,  if  it  were  not  that  the 
world  at  large  seizes  the  character  of  an  asserted  fact  better  than 
that  of  a  mode  of  inference,     A  grand  step  towards  the  deifica- 
cation  of  a  lady,  made  by  alleged   revelation   1800  years  after 
her  death,  is  of  glaring  evidence  :  two  or  three  additional  shiffle- 
shuffles  towards  defence  of  saying  the  Athanasian  curse  in  church 
and  unsaying  it  out  of  church,  are   hardly  noticed.     Swift  has 
bungled  his  satire  where  he  makes  Peter  a  party  to  finding  out 
what  he  wants,  totidem   syllabis  and  totidem  literis,  when  he 
cannot  find  it  totidem  verbis.     This  is  Protestant  method  :  the 
Eoman    plan    is   viam  faciam ;    the    Protestant    plan  is  viam 
inveniam.     The  public  at  large  begins  to  be  conversant  with  the 
ways  of  ivriggling  out,  as  shown  in  the  interpretations  of  the 
damnatory  parts  of  the  Athanasian  Creed,  the  phrases  of  the  Burial 
Service,  &c.     The  time  will  come  when  the  same    public  will 
begin  to  see  the  ways  of  ivriggling  in.  But  one  thing  at  a  time : 


272  A  BUDGET  OF  PAKADOXES. 

neither  Papal  Rome  nor  Protestant  Rome  was  built — nor  will 
be  pulled  down — in  a  day. 

The  distinction  above  drawn  between  the  two  great  antitheses 
of  Christendom  may  be  illustrated  as  follows.  Two  sets  of  little 
general  dealers  lived  opposite  to  one  another :  all  sold  milk. 
Each  vaunted  its  own  produce :  one  set  said  that  the  stuff  on  the 
other  side  the  way  was  only  chalk  and  water ;  the  other  said  that 
the  opposites  sold  all  sorts  of  filth,  of  which  calves'  brain  was  the 
least  nasty.  Now  the  fact  was  that  both  sets  sold  milk,  and  from 
the  same  dairy :  but  adulterated  with  different  sorts  of  dirty 
water :  and  both  honestly  believed  that  the  mixture  was  what 
they  were  meant  to  sell  and  ought  to  sell.  The  great  difference 
between  them,  about  which  the  apprentices  fought  each  other 
like  Trojans,  was  that  the  calves'  brain  men  poured  milk  into  the 
water,  and  the  chalk  men  poured  water  into  the  milk.  The 
Greek  and  Roman  sects  on  one  side,  the  Protestant  sects  on  the 
other,  must  all  have  churches  :  the  Greek  and  Roman  sects  pour 
the  New  Testament  into  their  churches  ;  the  Protestant  sects 
pour  their  churches  into  the  New  Testament.  The  Greek  and 
Roman  insist  upon  the  New  Testament  being  no  more  than  part 
and  parcel  of  their  churches  :  the  Protestant  insist  upon  their 
churches  being  as  much  part  and  parcel  of  the  New  Testament. 
All  dwell  vehemently  upon  the  doctrine  that  there  must  be  milk 
somewhere  ;  and  each  says — I  have  it.  The  doctrine  is  true  : 
and  can  be  verified  by  anyone  who  can  and  will  go  to  the  dairy 
for  himself.  Him  will  the  several  traders  declare  to  have  no 
milk  at  all.  They  will  bring  their  own  wares,  and  challenge  a 
trial :  they  want  nothing  but  to  name  the  judges.  To  vary  the 
metaphor,  those  who  have  looked  at  Christianity  in  open  day, 
know  that  all  who  see  it  through  painted  windows  shut  out  much 
of  the  light  of  heaven  and  colour  the  rest ;  it  matters  nothing 
that  the  stains  are  shaped  into  what  are  meant  for  saints  and 
angels. 

But  there  is  another  side  of  the  question.  To  decompose 
any  substance,  it  must  be  placed  between  the  poles  of  the  battery. 
Now  theology  is  but  one  pole  ;  philosophy  is  the  other.  No  one 
can  make  out  the  combinations  of  our  day  unless  he  read  the 
writings  both  of  the  priest  and  the  philosopher  :  and  if  any  one 
should  hold  the  first  word  offensive,  I  tell  him  that  I  mean  both 
words  to  be  significant.  In  reading  these  writings,  he  will  need 
to  bring  both  wires  together  to  find  out  what  it  is  all  about. 
Time  was  when  most  priests  were  very  explicit  about  the  fate  of 
philosophers,  and  most  philosophers  were  very  candid  about  their 


THEOLOGY  AND   PHILOSOPHY.  273 

opinion  of  priests.  But,  though  some  extremes  of  the  old  sorts 
still  remain,  there  is  now,  in  the  middle,  such  a  fusion  of  the  two 
pursuits  that  a  plain  man  is  wofully  puzzled.  The  theologian 
writes  a  philosophy  which  seems  to  tell  us  that  the  New  Testa- 
ment is  a  system  of  psychology ;  and  the  philosopher  writes  a 
Christianity  which  is  utterly  unintelligible  as  to  the  question 
whether  the  Resurrection  be  a  fact  or  a  transcendental  allegory. 
What  between  the  theologian  who  assents  to  the  Athanasian 
denunciation  in  what  seems  the  sense  of  no  denunciation,  and 
the  philosopher  who  parades  a  Christianity  which  looks  like  no 
revelation,  there  is  a  maze  which  threatens  to  have  the  only 
possible  clue  in  the  theory  that  everything  is  something  else,  and 
nothing  is  anything  at  all.  But  this  is  a  paradox  far  beyond 
my  handling  :  it  is  a  Budget  of  itself. 

Religion  and  Philosophy,  the  two  best  gifts  of  Heaven,  set  up 
in  opposition  to  each  other  at  the  revival  of  letters  ;  and  never 
did  competing  tradesmen  more  grossly  misbehave.  Bad  wishes 
and  bad  names  flew  about  like  swarms  of  wasps.  The  Athanasian 
curses  were  intended  against  philosophers ;  who,  had  they  been 
a  corporation,  with  state  powers  to  protect  them,  would  have 
formulized  a  per  contra.  But  the  tradesmen  are  beginning  to 
combine  :  they  are  civil  to  each  other ;  too  civil  by  half.  I  speak 
especially  of  Great  Britain.  Old  theology  has  run  off  to  ritualism, 
much  lamenting,  with  no  comfort  except  the  discovery  that  the 
cloak  Paul  left  at  Troas  was  a  chasuble.  Philosophy,  which 
always  had  a  little  sense  sewed  up  in  its  garments — to  pay  for  its 
funeral  ? — has  expended  a  trifle  in  accommodating  itself  to  the 
new  system.  But  the  two  are  poles  of  a  battery  ;  and  a  question 
arises. 

If  Peter  Piper  picked  a  peck  of  pepper, 

Where  is  the  peck  of  pepper  Peter  Piper  picked  ? 

If  Religion  and  Philosophy  be  the  two  poles  of  a  battery,  whose 
is  the  battery  Religion  and  Philosophy  have  been  made  the  poles 
of?  Is  the  change  in  the  relation  of  the  wires  any  presumption 
of  a  removal  of  the  managers?  We  know  pretty  well  who 
handled  the  instrument :  has  he  resigned  or  been  '  turned  out  ? 
Has  he  been  put  under  restriction  ?  A  fool  may  ask  more 
questions  than  twenty  sages  can  answer  :  but  there  is  hope  ;  for 

1  The  notion  that  the  Evil  Spirit  is  a  functionary  liable  to  be  dismissed  for  not 
attending  to  his  duty,  is,  so  far  as  my  reading  goes,  utterly  unknown  in  theology. 
My  first  wrinkle  on  the  siibject  was  the  remark  of  the  Somersetshire  farmer  upon 
Palmer  the  poisoner — '  Well !  if  the  Devil  don't  take  he,  he  didn't  ought  to  be  allowed 
to  be  devil  uo  longer.' 

T 


274  A   BUDGET   OF  PARADOXES. 

twenty  sages  cannot  ask  more  questions  than  one  reviewer  can 
answer.  I  should  like  to  see  the  opposite  sides  employed  upon 
the  question,  What  are  the  commoda,  and  what  the  pericula,  of 
the  current  approximation  of  Religion  and  Philosophy  ? 

All  this  is  very  profane  and  irreverent !  It  has  always  been  so 
held  by  those  whose  position  demands  such  holding.  To  describe 
the  Church  as  it  is  passes  for  assailing  the  Church  as  it  ought  to 
be  with  all  who  cannot  do  without  it.  In  Bedlam  a  poor  creature 
who  fancied  he  was  St.  Paul,  was  told  by  another  patient  that  he 
was  an  impostor;  the  first  maniac  lodged  a  complaint  against  the 
second  for  calling  St.  Paul  an  impostor,  which,  he  argued,  with 
much  appearance  of  sanity,  ought  not  to  be  permitted  in  a  well 
regulated  madhouse.  Nothing  could  persuade  him  that  he  had 
missed  the  question,  which  was  whether  he  was  St.  Paul.  The 
same  thing  takes  place  in  the  world  at  large.  And  especially 
must  be  noted  the  refusal  to  permit  to  the  profane  the  millionth 
part  of  the  licence  assumed  by  the  sacred.  I  give  a  sound 
churchman  the  epitaph  on  St.  John  Long  ;  the  usual  pronuncia- 
tion of  whose  name  must  be  noted — 

Behold  !  ye  quacks,  the  vengeance  strong 
On  deeds  like  yours  impinging  : 

For  here  below  lies  St.  John  Long 
Who  now  must  be  long  singeing. 

How  shameful  to  pronounce  this  of  the  poor  man  !  What,  Mr. 
Orthodox !  may  I  not  do  in  joke  to  one  pretender  what  you  do  in 
earnest — unless  you  quibble — to  all  the  millions  of  the  Ofreek 
Church,  and  a  great  many  others.  Enough  of  you  and  your 
reasoning !  Gro  and  square  the  circle  ! 

The  few  years  which  end  with  1867  have  shown,  not  merely 
the  intermediate  fusion  of  Theology  and  Philosophy  of  which  I 
have  spoken,  but  much  concentration  of  the  two  extremes,  which 
looks  like  a  gathering  of  forces  for  some  very  hard  fought 
Armageddon.  Extreme  theology  has  been  aiming  at  a  high 
Church  in  England,  which  is  to  show  a  new  front  to  all  heresy : 
and  extreme  philosophy  is  contriving  a  physical  organisation 
which  is  to  think,  and  to  show  that  mind  is  a  consequence  of 
matter,  or  thought  a  recreation  of  brain.  The  physical  speculators 
begin  with  a  possible  hypothesis,  in  which  they  aim  at  explana- 
tion :  and  so  the  bold  aspirations  of  the  author  of  the  '  Vestiges  ' 
find  standing-ground  in  the  variation  of  species  by  'natural 
selection.'  Some  relics — so  supposed — of  extremely  ancient  men 
are  brought  to  help  the  general  cause.  Only  distant  hints  are 
given  that  by  possibility  it  may  end  in  the  formation  of  all  living 


SCIENTIFIC  MATERIALISM.  275 

organisms  from  a  very  few,  if  not  from  one.  The  better  heads 
abovementioned  know  that  their  theory,  if  true,  does  not  bear 
upon  morals.  The  formation  of  solar  systems  from  a  nebular 
hypothesis,  followed  by  organisations  gradually  emerging  from 
some  curious  play  of  particles,  nay,  the  very  evolution  of  mind 
and  thought  from  such  an  apparatus,  are  all  as  consistent  with  a 
Personal  creative  power  to  whom  homage  and  obedience  are  due, 
and  who  has  declared  himself,  as  with  a  blind  Nature  of  Things. 
A  pure  materialist,  as  to  all  things  visible,  may  be  even  a  bigotted 
Christian :  this  is  not  frequent,  but  it  is  possible.  There  is  a 
proverb  which  says,  A  pig  may  fly,  but  it  isn't  a  likely  bird.  But 
when  the  psychological  speculator  comes  in,  he  often  undertakes 
to  draw  inferences  from  the  physical  conclusions,  by  joining  on 
his  tremendous  apparatus  of  a  priori  knowledge.  He  deduces 
that  he  can  do  without  a  God :  he  can  deduce  all  things  without 
any  such  necessity.  With  Occam  and  Newton  he  will  have  no 
more  causes  than  are  necessary  to  explain  phenomena  to  him : 
and  if  by  pure  head-work  combined  with  results  of  physical 
observation  he  can  construct  his  universe,  he  must  be  a  veiy 
unphilosophical  man  who  would  encumber  himself  with  a  useless 
Creator!  There  is  something  tangible  about  my  method,  says 
he ;  yours  is  vague.  He  requires  it  to  be  granted  that  his  system 
is  positive  and  that  your's  is  impositive.  So  reasoned  the  stage 
coachman  when  the  railroads  began  to  depose  him — '  If  you're 
upset  in  a  stage-coach,  why,  there  you  are !  but  if  you're  upset 
on  the  railroad,  where  are  you  ? '  The  answer  lies  in  another 
question,  Which  is  most  positive  knowledge,  (rod  deduced  from 
man  and  his  history,  or  the  postulates  of  the  few  who  think  they 
can  reason  a  priori  on  the  tacit  assumption  of  unlimited  command 
of  data  ? 

We  are  not  yet  come  to  the  existence  of  a  school  of  philoso- 
phers who  explicitly  deny  a  Creator :  but  we  are  on  the  way, 
though  common  sense  may  interpose.  There  are  always  straws 
which  show  the  direction  of  the  wind.  I  have  before  me  the 
printed  letter  of  a  medical  man — to  whose  professional  ability  I 
have  good  testimony — who  finds  the  vital  principle  in  highly 
rarefied  oxygen.  With  the  usual  logic  of  such  thinkers,  he  dis- 
misses the  '  eternal  personal  identity '  because  '  If  soul,  spirit, 
mind,  which  are  merely  modes  of  sensation,  be  the  attribute  or 
function  of  nerve-tissue,  it  cannot  possibly  have  any  existence 
apart  from  its  material  organism  ! '  How  does  he  know  this  im- 
possibility ?  If  all  the  mind  we  know  be  from  nerve-tissue,  how 
does  it  appear  that  mind  in  other  planets  may  not  be  another 

T  -2 


276  A  BUDGET  OF  PARADOXES. 

thing  ?  Nay,  when  we  '  come  to  possibilities,  does  not  his  own 
system  give  a  queer  one?  If  highly  rarefied  oxygen  be  vital 
power,  more  highly  rarefied  oxygen  may  be  more  vital  and  more 
powerful.  Where  is  this  to  stop  ?  Is  it  impossible  that  a  finite 
quantity,  rarefied  ad  infinitum,  may  be  an  Omnipotent  ?  Perhaps 
the  true  Genesis,  when  written,  will  open  with  '  In  the  beginning 
was  an  imperial  quart  of  oxygen  at  60°  of  -Fahrenheit,  and  the 
pressure  of  the  atmosphere  ;  and  this  oxygen  was  infinitely  rare- 
fied ;  and  this  oxygen  became  God.'  For  myself,  my  aspirations 
as  to  this  system  are  Manichaean.  The  quart  of  oxygen  is  the 
Ormuzd,  or  good  principle :  another  quart,  of  hydrogen,  is  the 
Ahriman,  or  evil  principle  !  My  author  says  that  his  system 
explains  Freewill  and  Immortality  so  obviously  that  it  is  difficult 
to  read  previous  speculations  with  becoming  gravity.  My  de- 
duction explains  the  conflict  of  good  and  evil  with  such  clearness 
that  no  one  can  henceforward  read  the  New  Testament  with 
becoming  reverence.  The  surgeon  whom  I  have  described  is  an 
early  bud  which  will  probably  be  nipped  by  the  frost  and  wither 
on  the  ground :  but  there  is  a  good  crop  coming.  Material 
pneuma  is  destined  to  high  functions ;  and  man  is  to  read  by 
gas-light. 

The  solar  system  truly  solved  :  demonstrating  by  the  perfect 
harmony  of  the  planets,  founded  on  the  four  universal  laws,  the 
Sun  to  be  an  electrical  space  ;  and  a  source  of  every  natural 
production  displayed  throughout  the  solar  system.  By  James 
Hopkins.  London,  1849,  8vo. 

The  author  says  : — 

'  I  am  satisfied  that  I  have  given  the  true  laws  constituting  the  Sun 
to  be  space ;  and  I  call  upon  those  disposed  to  maintain  the  contrary,  to 
give  true  laws  showing  him  to  be  a  body:  until  such  can  be  satis- 
factorily established,  I  have  an  undoubted  claim  to  the  credit  of  my 
theory, — That  the  Sun  is  an  Electric  Space,  fed  and  governed  by  the 
planets,  which  have  the  property  of  attracting  heat  from  it ;  and  the 
means  of  supplying  the  necessary  pabulum  by  their  degenerated  air 
driven  off  towards  the  central  space — the  wonderful  alembic  in  which 
it  becomes  transmuted  to  the  revivifying  necessities  of  continuous 
action ;  and  the  central  space  or  Sun  being  perfectly  electric,  has  the 
counter  property  of  repulsing  the  bodies  that  attract  it.  How  wonder- 
ful a  conception }  How  beautiful,  how  magnificent  an  arrangement  ! 

'  O  Centre  !  O  Space  !  0  Electric  Space ! ' 

1849.  Joseph  Ady  is  entitled  to  a  place  in  this  list  of  dis- 
coverers :  his  great  fault,  like  that  of  some  others,  lay  in  pushing 
his  method  too  far.  He  began  by  detecting  unclaimed  dividends. 


JOSEPH   ADY — ZADKIEL.  277 

and  disclosing  them  to  their  right  owners,  exacting  his  fee  before 
he  made  his  communication.  He  then  generalized  into  trying  to 
get  fees  from  all  of  the  name  belonging  to  a  dividend  ;  and  he 
gave  mysterious  hints  of  danger  impending.  For  instance,  he 
would  write  to  a  clergyman  that  a  legal  penalty  was  hanging 
over  him ;  and  when  the  alarmed  divine  forwarded  the  sum 
required  for  disclosure,  he  was  favoured  with  an  extract  from 
some  old  statute  or  canon,  never  repealed,  forbidding  a  clergyman 
to  be  a  member  of  a  corporation,  and  was  reminded  that  he  had 

insured  his  life  in  the Office,  which  had  a  royal  charter. 

He  was  facetious,  was  Joseph :  he  described  himself  in  his 
circulars  as  '  personally  known  to  Sir  Peter  Laurie  and  all  other 
aldermen ' ;  which  was  nearly  true,  as  he  had  been  before  most  of 
them  on  charges  of  false  pretence  ;  but  I  believe  he  was  nearly 
always  within  the  law.  Sir  James  Duke,  when  Lord  Mayor, 
having  particularly  displeased  him  by  a  decision,  his  circulars  of 
1849  contain  the  following  : — 

'  Should  you  have  cause  to  complain  of  any  party,  Sir  J.  Dake  has 
contrived  a  new  law  of  evidence,  viz.,  write  to  him,  he  will  consider 
your  letter  sufficient  proof,  and  make  the  parties  complained  of  pay 
without  judge  or  jury,  and  will  frank  you  from  every  expense.' 

I  strongly  suspect  that  Joseph  Ady  believed  in  himself. 

He  sometimes  issued  a  second  warning,  of  a  Sibylline  charac- 
ter : — 

'  Should  you  find  cause  to  complain  of  anybody,  my  voluntary 
referee,  the  Rt.  Hon.  Sir  Peter  Laurie,  Kt.,  perpetual  Deputy  Lord 
Mayer,  will  see  justice  done  you  without  any  charge  whatever :  he  and 

his  toady, .  The  accursed  of  Moses  can  hang  any  man : 

thus,  by  catching  him  alone  and  swearing  Nabotli  spake  evil  against 
God  and  the  King.  Therefore  (!)  I  admit  no  strangers  to  a  personal 
conference  without  a  prepayment  of  20s.  each.  Had  you  attended  to 
my  former  notice  you  would  have  received  twice  as  much :  neglect  this 
and  you  will  lose  all.' 

Zadkiel's  Almanac  for  1849.     Nineteenth  number. 

Raphael's  Prophetic  Almanac  for  1849.     Twenty-ninth  number. 

Reasons   for   belief  in  judicial   astrology,   and   remarks   on   the 

dangerous  character  of  popish  priestcraft.     London,  1849, 12mo. 
Astronomy  in  a  nutshell :  or  the  leading  problems  of  the   solar 

system   solved  by  simple   proportion  only,  on  the    theory  of 

magnetic  attraction.     By  Lieut.  Morrison,  R.N.    London  (s.  a.) 

12mo. 

Lieut.  Morrison  is  Zadkiel  Tao  Sze,  and  declares  himself  in 
real  earnest  an  astrologer.  There  are  a  great  many  books  on 


278  A  BUDGET   OF  PARADOXES. 

astrology,  but  I  have  not  felt  interest  enough  to  preserve  many 
of  them  which  have  come  in  my  way.  If  anything  ever  had  a 
fair  trial,  it  was  astrology.  The  idea  itself  is  natural  enough. 
A  human  being,  set  down  on  this  earth,  without  any  tradition, 
would  probably  suspect  that  the  heavenly  bodies  had  something 
to  do  with  the  guidance  of  affairs.  I  think  that  any  one  who 
tries  will  ascertain  that  the  planets  do  not  prophesy :  but  if  he 
should  find  to  the  contrary,  he  will  of  course  go  on  asking.  A 
great  many  persons  class  together  belief  in  astrology  and  belief 
in  apparitions :  the  two  things  differ  in  precisely  the  way  in 
which  a  science  of  observation  differs  from  a  science  of  experi- 
ment. Many  make  the  mistake  which  M.  le  Marquis  made  when 
he  came  too  late,  and  hoped  M.  Cassini  would  do  the  eclipse  over 
again  for  his  ladies.  The  apparition  chooses  its  own  time,  and 
comes  as  seldom  or  as  often  as  it  pleases,  be  it  departed  spirit, 
nervous  derangement,  or  imposition.  Consequently  it  can  only 
be  observed,  and  not  experimented  upon.  But  the  heavens,  if 
astrology  be  true,  are  prophesying  away  day  and  night  all  the 
year  round,  and  about  every  body.  Experiments  can  be  made, 
then,  except  only  on  rare  phenomena,  such  as  eclipses:  anybody 
may  choose  his  time  and  his  question.  This  is  the  great  differ- 
ence :  and  experiments  were  made,  century  after  century.  If 
astrology  had  been  true,  it  must  have  lasted  in  an  ever-improving 
state.  If  it  be  true,  it  is  a  truth,  and  a  useful  truth,  which  had 
experience  and  prejudice  both  in  its  favour,  and  yet  lost  ground 
as  soon  as  astronomy,  its  working  tool,  began  to  improve. 

1850.  A  letter  in  the  handwriting  of  an  educated  man,  dated 
from  a  street  in  which  it  must  be  taken  that  educated  persons 
live,  is  addressed  to  the  Secretary  of  the  Astronomical  Society 
about  a  matter  on  which  the  writer  says  '  his  professional  pursuit 
will  enable  him  to  give  a  satisfactory  reply.'  In  a  question  before 
a  court  of  law  it  is  sworn  on  one  side  that  the  moon  was  shining 
at  a  certain  hour  of  a  certain  night  on  a  certain  spot  in  London  ; 
on  the  o'her  side  it  is  affirmed  that  she  was  clouded.  The 
Secretary  is  requested  to  decide.  This  is  curious,  as  the  question 
is  not  astrological.  Persons  still  send  to  Greenwich.,  now  and 
then,  to  have  their  fortunes  told.  In  one  case,  not  very  many 
years  ago,  a  young  gentleman  begged  to  know  who  his  wife  was 
to  be,  and  what  fee  he  was  to  remit. 

Sometimes  the  astronomer  turns  conjurer  for  fun,  and  his 
prophecies  are  fulfilled.  It  is  related  of  Flamsteed  that  an  old 
woman  came  to  know  the  whereabouts  of  a  bundle  of  linen  which 


ASTROLOGY — COINCIDENCES.  279 

li;ul  strayed.     Flamsteed  drew  a  circle,  put  a  square  into  it,  and 
gravely  pointed  out  a  ditch,  near  her  cottage,  in  which  he  said  it 
would  be  found.     He  meant  to   have  ^iven  the  woman  a   little 
good  advice  when  she  came  back  :  but  she  came  back  in  great 
delight,  with  the  bundle  in  her  hand,  found  in  the  veiy  place. 
The  late  Baron   Zach   received  a  letter  from  Pons,  a  successful 
finder  of  comets,  complaining  that  for  a  certain  period  he  had 
found  no  comets,  though  he  had  searched  diligently.     Zach,  a 
man  of  much  sly  humour,  told  him  that  no  spots  had  been  seen 
on  the   sun  for   about   the    same   time — which  was   true, — and 
assured  him  that  when  the  spots  came  back,  the  comets  would 
come  with  them.     Some  time  after  he  got  a  letter  from  Pons, 
who  informed  him  with  great  satisfaction  that  he  was  quite  right, 
that  very  large  spots  had  appeared  on  the  sun,  and  that  he  had 
found  a  fine  comet  shortly  after.     I  do  not  vouch  for  the  first 
story,  but  I  have  the  second  in  Zach's  handwriting.     It  would 
mend  the  joke  exceedingly  if  some  day  a  real  relation  should  be 
established  between  comets  and  solar  spots  :  of  late  years  good 
reason  has  been  shown  for  advancing  a  connexion  between  these 
spots  and  the  earth's  magnetism.     If  the  two  things  had  been  put 
to  Zach,  he  would  probably  have  chosen  the  comets.     Here  is  a 
hint  for  a  paradox :  the  solar  spots  are  the  dead  comets,  which 
have  parted  with  their  light  and  heat  to  feed  the  sun,  as  was 
once  suggested.     I  should  not  wonder  if  I  were  too  late,  and  the 
tiling  had  been  actually  maintained.     My  list  does  not  contain 
the  twentieth  part  of  the  possible  whole. 

The  mention  of  coincidences  suggests  an  everlasting  source  of 
explanations,  applicable  to  all  that  is  extraordinary.  The  great 
paradox  of  coincidence  is  that  of  Leibnitz,  known  as  the •  pre-estab- 
lished harmony,  or  law  of  coincidences,  by  which,  separately 
and  independently,  the  body  receives  impressions,  and  the  mind 
proceeds  as  if  it  had  perceived  them  from  without.  Every  sensa- 
tion, and  the  consequent  state  of  the  soul,  are  independent  things 
01  incident  in  time  by  the  pre-established  law.  The  philosopher 
could  not  otherwise  account  far  the  connexion  of  mind  and 
matter  ;  and  he  never  goes  by  so  vulgar  a  rule  as  Wlxiferer  is,  is ; 
to  him  that  which  is  not  clear  as  to  how,  is  not  at  all.  Philoso- 
phers in  general,  who  tolerate  each  other's  theories  much  better 
than  Christians  do  each  other's  failings,  seldom  revive  Leibnitz's 
fantasy :  they  seem  to  act  upon  the  maxim  quoted  by  Father 
Eustace  from  the  Decretals,  Fadnora  osi^n<li  dam  punientur, 
jliKJttlii  diift'in  <ilf«'<in<l'i  (Ifhnif. 

The  great  ghost-paradox,  ai.d  its  tluoryof  <•<•  •••>-,  will 


280  A   BUDGET  OF  PAEADOXES. 

rise  to  the  surface  in  the  mind  of  everyone.     But  the  use  of  the 
word  coincidence  is  here  at  variance  with  its  common  meaning. 
When  A  is  constantly  happening,  and  also  B,  the   occurrence  of 
A  and  B  at  the  same  moment  is  the  mere  coincidence  which  may 
be  casualty.      But    the  case   before  us  is   that  A  is    constantly 
happening,  while  B,  when  it  does  happen,  almost  always  happens 
with  A,  and  very  rarely  without  it.     That  is  to   say,  such  is  the 
phenomenon  asserted  :  and  all  who  rationally  refer  it  to  casualty, 
affirm  that  B  is  happening  very  often  as  well  as  A,  but  that  it 
is  not  thought  worthy  of  being  recorded  except  when  A  is  simul- 
taneous.    Of  course  A  is  here  a  death,  and  B  the  spectral  appear- 
ance of  the    person  who   dies.     In    talking  of  this  subject  it  is 
necessary  to  put  out  of  the  question  all  who  play  fast  and  loose 
with  their  secret  convictions :  these  had  better  give  us  a  reason, 
when  they  feel  internal  pressure  for  explanation,  that  there  is  no 
weathercock  at  Kilve  ;  this  would  do  for  all  cases.     But  persons 
of  real  inquiry  will  see  that  first,  experience  does  not  bear  out 
the  asserted  frequency  of  the  spectre,  without  the  alleged  coinci- 
dence of  death :  and  secondly,  that  if  the  crowd  of  purely  casual 
spectres  were  so  great  that  it  is  no  wonder  that,  now  and   then 
the  person  should  have  died  at  or  near  the  moment,  we  ought  to 
expect    a  much  larger  proportion  of  cases  in  which  the  spectre 
should  come  at  the  moment  of  the  death  of  one  or  another  of  all 
the  cluster  who  are  closely  connected  with  the  original  of  the 
spectre.     But  this,  we  know,  is  almost  without  example.     It  re- 
mains   then,   for   all,  who    speculate   at   all,  to  look  upon  the 
asserted  phenomenon,  think  what  they  may  of  it,  the  thing  which 
is  to  be  explained,  as  a  connexion  in  time  of  the  death,  and  the 
simultaneous  appearance  of  the  dead.     Any  person  the  least  used 
to  the  theory  of  probabilities  will  see  that  purely  casual  coinci- 
dence, the  wrong   spectre  being  comparatively  so  rare  that  it 
may  be  said  never  to  occur,  is  not  within  the  rational  field  of 
possibility. 

The  purely  casual  coincidence,  from  which  there  is  no  escape 
except  the  actual  doctrine  of  special  providences,  carried  down  to 
a  very  low  point  of  special  intention,  requires  a  junction  of  the 
things  the  like  of  each  of  which  is  always  happening.  I  will 
give  three  instances  which  have  occurred  to  myself  within  the 
last  few  years  :  I  solemnly  vouch  for  the  literal  truth  of  every 
part  of  all  three  : 

In  August  1861,  M.  Senarmont,  of  the  French  Institute, 
wrote  to  me  to  the  effect  that  Fresnel  had  sent  to  England,  in  or 
shortly  after  1824,  a  paper  for  translation  and  insertion  in  the 


CUKIOUS   COINCIDENCES.  281 

European  Revieiv,  which  shortly  afterwards  expired.  The 
question  was  what  had  become  of  that  paper.  I  examined 
the  Eeview  at  the  Museum,  found  no  trace  of  the  paper,  and 
wrote  back  to  that  effect  at  the  Museum,  adding  that  everything 
now  depended  on  ascertaining  the  name  of  the  editor,  and  tracing 
his  papers  :  of  this  I  thought  there  was  no  chance.  I  posted  this 
letter  on  my  way  home,  at  a  Post  Office  in  the  Hampstead  Eoad 
at.  the  junction  with  Edward  Street,  on  the  opposite  side  of  which 
is  a  bookstall.  Lounging  for  a  moment  over  the  exposed  books, 
sicut  meus  est  inos,  I  saw,  within  a  few  minutes  of  the  posting 
of  the  letter,  a  little  catch-penny  book  of  anecdotes  of  Macaulay, 
which  I  bought,  and  ran  over  for  a  minute.  My  eye  was  soon 
caught  by  this  sentence  : — '  One  of  the  young  fellows  immediately 
wrote  to  the  editor  (Mr.  Walker)  of  the  European  Review.'  I 
thus  got  the  clue  by  which  I  ascertained  that  there  was  no  chance 
of  recovering  Fresnel's  paper.  Of  the  mention  of  current 
reviews,  not  one  in  a  thousand  names  the  editor. 

In  the  summer  of  1865  I  made  my  first  acquaintance  with  the 
tales  of  Nathaniel  Hawthorne,  and  the  first  I  read  was  about  the 
siege  of  Boston  in  the  War  of  Independence.  I  could  not  make 
it  out :  everybody  seemed  to  have  got  into  somebody  else's  place. 
I  was  beginning  the  second  tale,  when  a  parcel  arrived  :  it  was 
a  lot  of  old  pamphlets  and  other  rubbish,  as  he  called  it,  sent  by 
a  friend  who  had  lately  sold  his  books,  had  not  thought  it  worth 
while  to  send  these  things  for  sale,  but  thought  I  might  like  to 
look  at  them  and  possibly  keep  some.  The  first  thing  I  looked 
at  was  a  sheet  which,  being  opened,  displayed  '  A  plan  of  Boston 
and  its  environs,  shewing  the  true  situation  of  his  Majesty's 
army  and  also  that  of  the  rebels,  drawn  by  an  engineer,  at  Boston 
Oct.  1775.'  Such  detailed  plans  of  current  sieges  being  then 
uncommon,  it  is  explained  that  4  The  principal  part  of  this  plan 
was  surveyed  by  Eichard  Williams,  Lieutenant  at  Boston  ;  and 
sent  over  by  the  son  of  a  nobleman  to  his  father  in  town,  by 
whose  permission  it  wa,s  published.'  I  immediately  saw  that  my 
confusion  arose  from  my  supposing  that  the  king's  troops  were 
besieging  the  rebels,  when  it  was  just  the  other  way. 

April  1,  1853,  while  engaged  in  making  some  notes  on  a  logical 
point,  an  idea  occurred  which  was  perfectly  new  to  me,  on  the 
mode  of  conciliating  the  notions  of  omnipresence  and  indivivibi- 
lil>/  into  parts.  What  it  was  is  no  matter  here:  suffice  it  that, 
since  it  was  published  elsewhere  (in  a  paper  on  Infinity.,  Camb. 
Phil.  Trans,  vol.  xi.  p.  1)  I  have  not  had  it  produced  to  me.  I 
had  just  finished  a  paragraph  on  the  subject,  when  a  parcel  came 


282  A  BUDGET  OF  PAKADOXES. 

in  from  a  bookseller  containing  Heywood's  '  Analysis  of  Kant's 
Critick,'  1844.  On  turning  over  the  leaves  I  found  (,p.  109)  the 
identical  thought  which  up  to  this  day,  I  only  know  as  in  my 
own  paper,  or  in  Kant.  I  feel  sure  I  had  not  seen  it  before,  for 
it  is  in  Kant's  first  edition,  which  was  never  translated  to  my 
knowledge ;  and  it  does  not  appear  in  the  later  editions.  Mr. 
Hey  wood  gives  some  account  of  the  first  edition. 

In  the  broadsheet  which  gave  account  of  the  dying  scene  of 
Charles  II.,  it  is  said  that  the  Koman  Catholic  priest  was  intro- 
duced by  P.  M.  A.  C.  F.  The  chain  was  this :  the  Duchess  of 
Portsmouth  applied  to  the  Duke  of  York,  who  may  have  consulted 
his  Cordelier  confessor,  Mansuete,  about  procuring  a  priest,  and 
the  priest  was  smuggled  into  the  king's  room  by  the  Duchess  and 
Chiffinch.  Now  the  letters  "are  a  verbal  acrostic  of  Pere  Mansuete 
a  Cordelier  Friar,  and  a  syllabic  acrostic  of  PortsMouth  and 
Chif Finch.  This  is  a  singular  coincidence.  Macaulay  adopted 
the  first  interpretation,  preferring  it  to  the  second,  which  I 
brought  before  him  as  the  conjecture  of  a  near  relative  of  my 
own.  But  Mansuete  is  not  mentioned  in  his  narrative :  it  may 
well  be  doubted  whether  the  writer  of  a  broadside  for  English 
readers  would  use  Pere  instead  of  Father.  And  the  person  who 
really  '  reminded '  the  Duke  of  '  the  duty  he  owed  to  his  brother,' 
was  the  Duchess  and  not  Mansuete.  But  my  affair  is  only  with 
the  coincidence. 

But  there  are  coincidences  which  are  really  connected  without 
the  connexion  being  known  to  those  who  find  in  them  matter  of 
astonishment.  Presentiments  furnish  marked  cases:  sometimes 
there  is  no  mystery  to  those  who  have  the  clue.  In  the  Gentle- 
man's Magazine  (vol.  80,  part  2,  p.  33)  we  read,  the  subject 
being  presentiment  of  death,  as  follows  :— '  In  1778,  to  come 
nearer  the  recollection  of  survivors,  at  the  taking  of  Pondicherry, 
Captain  John  Fletcher,  Captain  De  Morgan,  and  Lieutenant 
Bosanquet,  each  distinctly  foretold  his  own  death  on  the  morning 
of  his  fate.'  I  have  no  doubt  of  all  three  ;  and  I  knew  it  of  my 
grandfather  long  before  I  read  the  above  passage.  He  saw  that 
the  battery  he  commanded  was  unduly  exposed  :  I  think  by  the 
sap  running  through  the  fort  when  produced.  He  represented 
this  to  the  engineer  officers,  and  to  the  commander-in-chief ;  the 
engineers  denied  the  truth  of  the  statement,  the  commander 
believed  them,  my  grandfather  quietly  observed  that  he  must 
make  his  will,  and  the  French  fulfilled  his  prediction.  His  will 
bore  date  the  day  of  his  deatli ;  and  I  always  thought  it  more 
remarkable  than  the  fulfilment  of  the  prophecy  that  a  soldier 


.COINCIDENCE — BETTING.  283 

should  not  consider  any  danger  short  of  one  like  the  above,  suffi- 
cient reason  to  make  his  will.  I  suppose  the  other  officers  were 
similarly  posted.  I  am  told  that  military  men  very  often  defer 
making  their  wills  until  just  before  an  action :  but  to  face  the 
ordinary  risks  intestate,  and  to  wait  until  speedy  death  must  be 
the  all  but  certain  consequence  of  a  stupid  mistake,  is  carrying 
the  principle  very  far.  In  the  matter  of  coincidences  there  are, 
as  in  other  cases,  two  wonderful  extremes  with  every  intermediate 
degree.  At  one  end  we  have  the  confident  people  who  can 
attribute  anything  to  casual  coincidence ;  who  allow  Zadok 
Imposture  and  Nathan  Coincidence  to  anoint  Solomon  Self- 
conceit  king.  At  the  other  end  we  have  those  who  see  some- 
thing very  curious  in  any  coincidence  you  please,  and  whose 
minds  yearn  for  a  deep  reason.  A  speculator  of  this  class 
happened  to  find  that  Matthew  viii.  28-33  and  Luke  viii.  26-33 
contain  the  same  account,  that  of  the  demons  entering  into  the 
swine.  Very  odd  !  chapters  tallying,  and  verses  so  nearly  :  is  the 
versification  rightly  managed  ?  Examination  is  sure  to  show 
that  there  are  monstrous  inconsistencies  in  the  mode  of  division, 
which  being  corrected,  the  verses  tally  as  well  as  the  chapters. 
And  then  how  comes  it  ?  I  cannot  go  on,  for  I  have  no  gift  at 
torturing  a  coincidence  ;  but  I  would  lay  twopence,  if  I  could 
make  a  bet — which  I  never  did  in  all  my  life — that  some  one  or 
more  of  my  readers  will  try  it.  Some  people  say  that  the  study 
of  chances  tends  to  awaken  a  spirit  of  gambling  :  I  suspect  the 
contrary.  At  any  rate,  I  myself,  the  writer  of  a  mathematical 
book  and  a  comparatively  popular  book,  have  never  laid  a  bet 
nor  played  for  a  stake,  however  small :  not  one  single  time. 

It  is  useful  to  record  such  instances  as  I  have  given,  with 
precision  and  on  the  solemn  word  of  the  recorder.  When  such  a 
story  as  that  of  Flamsteed  is  told,  a  priori  assures  us  that  it  could 
not  have  been  :  the  story  may  have  been  a  ben  trovato,  but  not 
the  bundle.  It  is  also  useful  to  establish  some  of  the  good  jokes 
which  all  take  for  inventions.  My  friend  Mr.  J.  Bellingham 
Inglis,  before  1800,  saw  the  tobacconist's  carriage  with  a  sample 
of  tobacco  in  a  shield,  and  the  motto  Quid  rides  (N  &  Q.,  3rd  S.  i. 
245).  His  father  was  able  to  tell  him  all  about  it.  The  tobac- 
conist was  Jacob  Brandon,  well  known  to  the  elder  Mr.  Inglis,  and 
the  person  who  started  the  motto,  the  instant  he  was  asked  for 
such  a  thing,  was  Harry  Calender  of  Lloyd's,  a  scholar  and  a  wit. 
My  friend  Mr.  H.  Crabb  Robinson  remembers  the  King's  Counsel 
(Samuel  Marryat)  who  took  the  motto  Causes  produce  effects^ 
when  his  success  enabled  him  to  start  a  carriage. 


284  A  BUDGET  OF  PAKADOXES, 

The  coincidences  of  errata  are  sometimes  very  remarkable  :  it 
may  be  that  the  misprint  has  a  sting.  The  death  of  Sir  W. 
Hamilton  of  Edinburgh  was  known  in  London  on  a  Thursday,  and 
the  editor  of  the  Athenceum  wrote  to  me  in  the  afternoon  for  a 
short  obituary  notice  to  appear  on  Saturday.  I  dashed  off  the 
few  lines  which  appeared  without  a  moment  to  think :  and  those 
of  my  readers  who  might  perhaps  think  me  capable  of  contriving 
errata  with  meaning  will,  I  am  sure,  allow  the  hurry,  the  occasion, 
and  my  own  peculiar  relation  to  the  departed,  as  sufficient  reasons 
for  believing  in  my  entire  innocence.  Of  course  I  could  not 
see  a  proof :  and  two  errata  occurred.  The  words  '  addition  to 
Stewart '  require  '/or  addition  to  read  edition  of.'  This  represents 
what  had  been  insisted  on  by  the  Edinburgh  publisher,  who, 
frightened  by  the  edition  of  Reid,  had  stipulated  for  a  simple 
reprint  without  notes.  Again  '  principles  of  logic  and  mathe- 
matics '  required  '/or  mathematics  read  metaphysics.'  No  four 
words  could  be  put  together  which  would  have  so  good  a  title  to 
be  Hamilton's  motto. 

April  1850,  found  in  the  letter-box,  three  loose  leaves,  well 
printed  and  over  punctuated,  being 

Chapter  VI.  Brethren,  lo  I  come,  holding  forth  the  word  of  life,  for 
so  I  am  commanded  ....  Chapter  VII.  Hear  my  prayer,  O 
generations  !  and  walk  by  the  way,  to  drink  the  waters  of  the 
river  ....  Chapter  VIII.  Hearken  o  earth,  earth,  earth,  and 
the  kings  of  the  earth,  and  their  armies  .... 

A  very  large  collection  might  be  made  of  such  apostolic 
writings.  They  go  on  well  enough  in  a  misty — meant  for  mysti- 
cal— imitation  of  St.  Paul  or  the  prophets,  until  at  last  some 
prodigious  want  of  keeping  shows  the  education  of  the  writer. 
For  example,  after  half  a  page  which  might  pass  for  Irving's 
preaching — though  a  person  to  whom  it  was  presented  as  such 
would  say  that  most  likely  the  head  and  tail  would  make  some- 
thing more  like  head  and  tail  of  it — we  are  astouaded  by  a 
declaration  from  the  Holy  Spirit,  speaking  of  himself,  that  he 
is  '  not  ashamed  of  the  Gospel  of  Christ.'  It  would  be  long  before 
we  should  find  in  educated  rhapsody — of  which  there  are  speci- 
mens enough — such  a  thing  as  a  person  of  the  Trinity  taking 
merit  for  moral  courage  enough  to  stand  where  St.  Peter  fell.  The 
following  declaration  comes  next — '  I  will  judge  between  cattle 
and  cattle,  that  use  their  tongues.' 


PERPETUAL  MOTION.  285 


The   figure   of  the  earth.     By  J.    L.    Murphy,  of  Birmingham. 
(London  and  Birmingham,  4  pages,  12mo.)  (1850  ?) 

Mr.  Murphy  invites  attention  and  objection  to  some  assertions, 
as  that  the  earth  is  prolate,  not  oblate.  '  If  the  philosopher's 
conclusion  be  right,  then  the  pole  is  the  centre  of  a  valley  (!) 
thirteen  miles  deep.'  Hence  it  would  be  very  warm.  It  is 
answer  enough  to  ask — Who  knows  that  it  is  not  ? 


A  paragraph   in   the  MS.  appears  to   have  been  inserted  in   this   place   by 
mistake     It  will  be  found  in  the  Appendix  at  the  end  of  this  volume. 


1851.  The  following  letter  was  written  by  one  of  a  class  of 
persons  whom,  after  much  experience  of  them,  I  do  not  pronounce 
insane.  But  in  this  case  the  second  sentence  gives  a  suspicion  of 
actual  delusion  of  the  senses  ;  the  third  looks  like  that  eye  for 
the  main  chance  which  passes  for  sanity  on  the  Stock  Exchange 
and  elsewhere : — 

15th  Sept.  1851. 

'  Gentlemen, — I  pray  you  take  steps  to  make  known  that  yesterday  I 
completed  my  invention  which  will  give  motion  to  every  country  on  the 
Earth; — to  move  Machinery! — the  long  sought  in  vain  'Perpetual 
Motion ' !  ! — I  was  supported  at  the  time  by  the  Queen  and  H.B.H. 
Prince  Albert.  If,  Gentlemen,  you  can  advise  me  how  to  proceed  to 
claim  the  reward,  if  any  is  offered  by  the  Government,  or  how  to  secure 
the  PATENT  for  the  machine,  or  in  any  way  assist  me  by  advice  in  this 
great  work,  I  shall  most  graciously  acknowledge  your  consideration. 

These  are  my  convictions  that  my  SEVERAL  discoveries  will  be 
realised :  and  this  great  one  can  be  at  once  acted  upon  :  although  at 
this  moment  it  only  exists  in  my  mind,  from  my  knowledge  of  certain 
fixed  principles  in  nature  : — the  Machine  I  have  not  made,  as  I  only 
completed  the  discovery  YESTERDAY,  Sunday  ! 

I  have,  &c. 
To  the  Directors  of  the 
London  University,  Gower  Street. 


286  A  BUDGET  OF  PARADOXES. 


The   Divine   Drama   of  History  and  Civilisation.     By  the  Rev. 
James  Smith,  M.A.     London,  1854,  8vo. 

I  have  several  books  on  that  great  paradox  of  our  day,  Spiri- 
tualism, but  I  shall  exclude  all  but  three.  The  bibliography  of 
this  subject  is  now  very  large.  The  question  is  one  both  of 
evidence  and  speculation  ; — Are  the  facts  true  ?  Are  they  caused 
by  spirits  ?  These  I  shall  not  enter  upon :  I  shall  merely  re- 
commend this  work  as  that  of  a  spiritualist  who  does  not  enter  on 
the  subject,  which  he  takes  for  granted,  but  applies  his  derived 
views  to  the  history  of  mankind  with  learning  and  thought.  Mr. 
Smith  was  a  man  of  a  very  peculiar  turn  of  thinking.  He  was, 
when  alive,  the  editor,  or  an  editor,  of  the  Family  Herald :  I 
say  when  alive,  to  speak  according  to  knowledge  ;  for,  if  his  own 
views  be  true,  he  may  have  a  hand  in  it  still.  The  answers  to 
correspondents,  in  his  time,  were  piquant  and  original  above  any 
I  ever  saw.  I  think  a  very  readable  book  might  be  made  out 
of  them,  resembling  '  Guesses  at  Truth  : '  the  turn  given  to  an 
inquiry  about  morals,  religion,  or  socials,  is  often  of  the  highest 
degree  of  unexpectedness  ;  the  poor  querist  would  find  himself 
right  in  a  most  unpalatable  way. 

Answers  to  correspondents,  in  newspapers,  are  very  often  the 
fag  ends  of  literature.  I  shall  never  forget  the  following.  A 
person  was  invited  to  name  a  rule  without  exception,  if  he  could : 
he  answered  '  A  man  must  be  present  when  he  is  shaved.'  A 
lady — what  right  have  ladies  to  decide  questions  about  shaving  ? 
— said  this  was  not  properly  a  rule  ;  and  the  oracle  was  consulted. 
The  editor  agreed  with  the  lady ;  he  said  that  '  a  man  must  be 
present  when  he  is  shaved '  is  not  a  rule,  but  a  fact. 

[Among  my  anonymous  communicants  is  one  who  states  that 
I  have  done  injustice  to  the  Rev.  James  Smith  in  'referring 
to  him  as  a  spiritualist,'  and  placing  his  '  Divine  Drama '  among 
paradoxes :  '  it  is  no  paradox,  nor  do  spiritualistic  views  mar  or 
weaken  the  execution  of  the  design.'  Quite  true :  for  the  design 
is  to  produce  and  enforce  '  spiritualistic  views ; '  and  leather  does 
not  mar  nor  weaken  a  shoemaker's  plan.  I  knew  Mr.  Smith 
well,  and  have  often  talked  to  him  on  the  subject :  but  more 
testimony  from  me  is  unnecessary  ;  his  book  will  speak  for  itself. 
His  peculiar  style  will  justify  a  little  more  quotation  than  is  just 
necessary  to  prove  the  point.  Looking  at  the  '  battle  of  opinion ' 
now  in  progress,  we  see  that  Mr.  Smith  was  a  prescient : — 


KEY.   JAMES   SMITH.  287 

(P.  588.)  '  From  the  general  review  of  parties  in  England, 
it  is  evident  that  no  country  in  the  world  is  better  prepared  for 
the  great  Battle  of  Opinion.  Where  else  can  the  battle  be 
fought  but  where  the  armies  are  arrayed  ?  And  here  they  all 
are,  Greek,  Eoman,  Anglican,  Scotch,  Lutheran,  Calvinist, 
Established  and  Territorial,  with  Baronial  Bishops,  and  Non- 
established  of  every  grade — churches  with  living  prophets  and 
apostles,  and  churches  with  dead  prophets  and  apostles,  and 
apostolical  churches  without  apostles,  and  philosophies  without 
either  prophets  or  apostles,  and  only  wanting  one  more,  "  the 
Christian  Church,"  like  Aaron's  rod,  to  swallow  up  and  digest 
them  all,  and  then  bud  and  flourish.  As  if  to  prepare  our  minds 
for  this  desirable  and  inevitable  consummation,  different  parties 
have  been  favoured  with  a  revival  of  that  very  spirit  of  revelation 
by  which  the  Church  itself  was  originally  founded.  There  is  a 
complete  series  of  spiritual  revelations  in  England  and  the 
United  States,  besides  mesmeric  phenomena  that  bear  a  re- 
semblance to  revelation,  and  thus  gradually  open  the  mind  of 
the  philosophical  and  infidel  classes,  as  well  as  the  professed 
believers  of  that  old  revelation  which  they  never  witnessed  in 
living  action,  to  a  better  understanding  of  that  Law  of  Nature 
(for  it  is  a  Law  of  Nature)  in  which  all  revelation  originates 
and  by  which  its  spiritual  communications  are  regulated.' 

Mr.  Smith  proceeds  to  say  that  there  are  only  thirty-five  in- 
corporated churches  -in  England,  all  formed  from  the  New  Testa- 
ment except  five,  to  each  of  which  five  he  concedes  a  revelation 
of  its  own.  The  five  are  the  Quakers,  the  Swedenborgians,  the 
Southcottians,  the  Irvingites,  and  the  Mormonites.  Of  Joanna 
Southcott  he  speaks  as  follows  : — 

(P.  592.)  '  Joanna  Southcott  is  not  very  gallantly  treated 
by  the  gentlemen  of  the  Press,  who,  we  believe,  without  knowing 
anything  about  her,  merely  pick  up  their  idea  of  her  character 
from  the  rabble.  We  once  entertained  the  same  rabble  idea  of 
her ;  but  having  read  her  works — for  we  really  have  read  them 
— we  now  regard  her  with  great  respect.  However,  there  is  a 
great  abvmdance  of  chaff  and  straw  to  her  grain ;  but  the  grain 
is  good,  and  as  we  do  not  eat  either  the  chaff  or  straw  if  we  can 
avoid  it,  nor  even  the  raw  grain,  but  thrash  it  and  winnow  it, 
and  grind  it  and  bake  it,  we  find  it,  after  undergoing  tins 
process,  not  only  very  palatable,  but  a  special  dainty  of  its  kind. 
But  the  husk  is  an  insurmountable  obstacle  to  those  learned  and 
educated  gentlemen  who  judge  of  books  entirely  by  the  style 


288  A  BUDGET   OF  PAEADOXES. 

and  the  grammar,  or  those  who  eat  grain  as  it  grows,  like  the 
cattle.  Such  men  would  reject  all  prological  revelation  ;  for 
there  never  was  and  probably  never  will  be  a  revelation  by  voice 
and  vision  communicated  in  classical  manner.  It  would  be  an 
invasion  of  the  rights  and  prerogatives  of  Humanity,  and  as 
contrary  to  the  Divine  and  the  Established  order  of  mundane 
government,  as  a  field  of  quartern  loaves  or  hot  French  rolls.' 

Mr.  Smith's  book  is  spiritualism  from  beginning  to  end ;  and 
my  anonymous  gainsayer,  honest  of  course,  is  either  ignorant  of 
the  work  he  thinks  he  has  read,  or  has  a  most  remarkable  develop- 
ment of  the  organ  of  imperception.] 

I  cut  the  following  from  a  Sunday  paper  in  1849  : — 

X.  Y. — The  Chaldeans  began  the  mathematics,  in  which  the 
Egyptians  excelled.  Then  crossing  the  sea,  by  means  of  Thales,  the 
Milesian,  they  came  into  Greece,  where  they  were  improved  very  much 
by  Pythagoras,  Anaxagoras,  and  Anopides  of  Chios.  These  were 
followed  by  Briso,  Antipho,  [two  circle- sq  ua  rer  s  ;  where  is  Euclid?] 
and  Hippocrates,  but  the  excellence  of  the  algebraic  art  was  begun  by 
Geber,  an  Arabian  astronomer,  and  was  carried  on  by  Cardanus,  Tarta- 
glia,  Clavius,  Sfcevinus,  Ghctaldus,  Herigenius,  Fran,  Van  Schooten 
[meaning  Francis  Van  Schooten],  Florida  de  Beaume,  &c. 

Bryso  was  a  mistaken  man.  Antipho  had  the  disadvantage  of 
being  in  advance  of  his  age.  He  had  the  notion  of  which  the 
modern  geometry  has  made  so  much,  that  of  a  circle  being  the 
polygon  of  an  infinitely  great  number  of  sides.  He  could  make 
no  use  of  it,  but  the  notion  itself  made  him  a  sophist  in  the 
eyes  of  Aristotle,  Eutocius,  &c.  Greber,  an  Arab  astronomer, 
and  a  reputed  conjurer  in  Europe,  seems  to  have  given  his  name 
to  unintelligible  language  in  the  word  gibberish.  At  one  time 
algebra  was  traced  to  him ;  but  very  absurdly,  though  I  have 
heard  it  suggested  that  algebra  and  gibberish  must  have  had  one 
inventor. 

Any  person  who  meddles  with  the  circle  may  find  himself  the 
crane  who  was  netted  among  the  geese  :  as  Antipho  for  one, 
and  Olivier  de  Serres  for  another.  This  last  gentleman  ascer- 
tained, by  weighing,  that  the  area  of  the  circle  is  very  nearly 
that  of  the  square  on  the  side  of  the  inscribed  equilateral 
triangle:  which  it  is,  as  near  as  3-162  ...  to  3-141.  .  .  .  He 
did  not  pretend  to  more  than  approximation  ;  but  Montucla  and 
others  misunderstood  him,  and,  still  worse,  misunderstood  their 
own  misunderstanding,  and  made  him  say  the  circle  was  exactly 


ST.   VITUS,   PATRON   OF   CYCLOMETERS.  289 

double  of  the  equilateral  triangle.  He  was  let  out  of  linibo  by 
Lacroix,  in  a  note  to  his  edition  of  Montucla's  History  of  Quad- 
rature. 

Quadratura  del  cercliio,  trisezione  dell'  angulo,  et  duplicazione  del 

cubo,    problem!    geometricamente    risolute     e   dimostrate    dal 

Beverendo    Arciprete    di    San   Vito   D.    Domenico   Anghera. 

Malta,  1854,  8vo. 
Equazioni  geometriche,  estratte  dalla  lettera  del  Rev.  Arciprete  .  . 

al  Professore  Pullicino   sulla  quadratura  del  cerchio.     Milan, 

1855  or  1856,  8vo. 
H  Mediterraneo  gazetta  di  Malta,  26  Decembre  1855,  No.  909 : 

also  911,  912,  913,  914,  936,  939. 
The  Malta  Times,  Tuesday,  9th  June  1857. 
Misura  esatta  del  cerchio,  dal  Rev.    D.  Anghera.     Malta,  1857, 

12mo. 
Quadrature  of  the  circle  ...  by  the  Rev.  D.  Anghera,  Archpriest 

of  St.  Vito.     Malta,  1858,  12mo. 

I  have  looked  for  St.  Vitus  in  catalogues  of  saints,  but  never 
found  his  legend,  though  he  figures  as  a  day-mark  in  the  oldest 
almanacs.  He  must  be  properly  accredited,  since  he  has  an  arch- 
priest.  And  I  pronounce  and  ordain,  by  right  accruing  from  the 
trouble  I  have  taken  in  this  subject,  that  he,  St.  Vitus,  who  leads 
his  votaries  a  never-ending  and  unmeaning  dance,  shall  henceforth 
be  held  and  taken  to  be  the  patron  saint  of  the  circle-squarer. 
His  day  is  the  15th  of  June,  which  is  also  that  of  St.  Modestus, 
with  whom  the  said  circle-squarer  often  has  nothing  to  do.  And  . 
he  must  not  put  himself  under  the  first  saint  with  a  slanten- 
dicular  reference  to  the  other,  as  is  much  to  be  feared  was  done 
by  the  Cardinal  who  came  to  govern  England  with  a  title  con- 
taining St.  Pudentiana,  who  shares  a  day  with  St.  Dunatan. 
The  Archpriest  of  St.  Vitus  will  have  it  that  the  square  inscribed 
in  a  semicircle  is  half  of  the  semicircle,  or  the  circumference 
3£  diameters.  He  is  active  and  able,  with  nothing  wrong  about 
him  except  his  paradoxes.  In  the  second  tract  named  he  has 
given  the  testimonials  of  crowned  heads  and  ministers,  &c.  as 
follows.  Louis-Napoleon  gives  thanks.  The  minister  at  Turin 
refers  it  to  the  Academy  of  Sciences,  and  hopes  so  much  labour 
will  be  judged  degna  di  preglo.  The  Vice-Chancellor  of  Oxford 
— a  blunt  Englishman — begs  to  say  that  the  University  has  never 
proposed  the  problem,  as  some  affirm.  The  Prince  Regent  of 
Baden  has  received  the  work  with  lively  interest.  The  Academy 
of  Vienna  is  not  in  a  position  to  enter  into  the  question.  The 

U 


290  A  BUDGET   OF  PARADOXES. 

Academy  of  Turin  offers  the  most  distinct  thanks.  The  Academy 
della  Crusca  attends  only  to  literature,  but  gives  thanks.  The 
Queen  of  Spain  has  received  the  work  with  the  highest  apprecia- 
tion. The  University  of  Salamanca  gives  infinite  thanks,  and 
feels  true  satisfaction  in  having  the  book.  Lord  Palmerston 
gives  thanks,  by  the  hand  of  '  William  San.'  The  Viceroy  of 
Egypt,  not  being  yet  up  in  Italian,  will  spend  his  first  moments 
of  leisure  in  studying  the  book,  when  it  shall  have  been  trans- 
lated into  French :  in  the  mean  time  he  congratulates  the  author 
upon  his  victory  over  a  problem  so  long  held  insoluble.  All  this 
is  seriously  published  as  a  rate  in  aid  of  demonstration.  If  these 
royal  compliments  cannot  make  the  circumference  of  a  circle 
about  2  per  cent,  larger  than  geometry  will  have  it — which  is 
all  that  is  wanted — no  wonder  that  thrones  are  shaky. 

I  am  informed  that  the  legend  of  St.  Vitus  is  given  by 
Eibadeneira  in  his  lives  of  the  Saints,  and  that  Baronius,  in  his 
Martyrologium  Romanum,  refers  to  several  authors  who  have 
written  concerning  him.  There  is  an  account  in  Mrs.  Jameson's 
'History  of  Sacred  and  Legendary  Art'  (ed.  of  1863,  p.  544). 
But  it  seems  that  St.  Vitus  is  the  patron  saint  of  all  dances ;  so 
that  I  was  not  so  far  wrong  in  making  him  the  protector  of  the 
cyclometers.  Why  he  is  represented  with  a  cock  is  a  disputed 
point,  which  is  now  made  clear :  next  after  gallus  gallinaceus 
himself,  there  is  no  crower  like  the  circle-squarer. 

The  following  is  an  extract  from  the  English  Cyclopaedia, 
Art.  TABLES  : — 

'  1853.  William  Shanks,  "  Contributions  to  Mathematics,  com- 
prising chiefly  the  Rectification  of  the  Circle  to  607  Places  of  Tables," 
London,  1853.  (QUADRATURE  OF  THE  CIRCLE.)  Here  is  a  table, 
because  it  tabulates  the  results  of  the  subordinate  steps  of  this 
enormous  calculation  as  far  as  527  decimals :  the  remainder  being 
added  as  results  only  during  the  printing.  For  instance,  one  step  is  the 
calculation  of  the  reciprocal  of  601. 5601  ;  and  the  result  is  given.  The 
number  of  pages  required  to  describe  these  results  is  87.  Mr.  Shanks 
has  also  thrown  off,  as  chips  or  splinters,  the  values  of  the  base  of 
Napier's  logarithms,  and  of  its  logarithms  of  2,  3,  5,  10,  to  137  deci- 
mals ;  and  the  value  of  the  modulus  '4342.  ...  to  136  decimals;  with 
the  13th,  25th,  37tli  ...  up  to  the  721st  powers  of  2.  These  tremen 
dous  stretches  of  calculation — at  least  we  so  call  them  in  our  day — are 
useful  in  several  respects  ;  they  prove  more  than  the  capacity  of  this 
or  that  computer  for  labour  and  accuracy  ;  they  show  that  there  is  in 
the  community  an  increase  of  skill  and  courage.  We  say  in  the 
community  :  we  fully  believe  that  the  unequalled  turnip  which  every 
now  and  then  appears  in  the  newspapers  is  a  sufficient  presumption 


MR,  SHANKS'   QUADRATURE.  291 

that  the  average  turnip  is  growing  bigger,  and  the  whole  crop  heavier. 
All  who  know  the  history  of  the  quadrature  are  aware  that  the  several 
increases  of  numbers  of  decimals  to  which  IT  has  been  carried  have 
been  indications  of  a  general  increase  in  the  power  to  calculate,  and  in 
courage  to  face  the  labour.  Here  is  a  comparison  of  two  different 
times.  In  the  day  of  Cocker,  the  pupil  was  directed  to  perform  a, 
common  subtraction  with  a  voice-accompaniment  of  this  kind :  "  7  from 

4  I  cannot,  but  add  10,  7  from  14  remains  7,  set  down  7  and  carry  1 ; 
8  and  1  which  I  carry  is  9,  9  from  2  I  cannot,  &c."      We  have  before 
us   the   announcement   of  the  following   table,  undated,    as   open   to 
inspection  at  the  Crystal  Palace,  Sydenham,  in  two  diagrams  of  7  ft. 
2  in.  by  6  ft.  6  in. : — "  The  figure  9  involved  into  the  912th  power,  and 
antecedent  powers  or  involutions,  containing  upwards  of  73,000  fignres. 
Also,  the  proofs  of  the  above,  containing  upwards  of  146,000  figures. 
By  Samuel  Fancourt,  of  Mincing  Lane,  London,  and  completed  by  him. 
in  the  year  1837,  at  the  age  of  sixteen.     N.B.  The  whole  operation 
performed  by  simple  arithmetic."      The  young  operator  calculated  by 
successive  squaring  the  2nd,  4th,  8th,  &c.,  powers  up  to  the  512th,  with 
proof  by  division.      But  511  multiplications  .by  9,  in  the  short  (or 
10-1)    way,  would  have  been  much  easier.     The  2nd,  32nd,  64th, 
128th,  256th,  and  512th  powers  are  given  at  the  back  of  the  announce- 
ment.    The  powers  of  2  have  been  calculated  for  many  purposes.      In 
vol.  ii.  of  his  "  Magia  Universalis  Nature  et  Artis,"  Herbipoli,  1658, 
4to.,  the  Jesuit   Gaspar  Schott  having  discovered,  on  some  grounds  of 
theological  magic,  that  the  degrees  of  grace  of  the  Virgin  Mary  were 
in  number  the  256th   power  of  2,  calculated  that  number.     Whether 
or   no  his    number    correctly  represented  the    result    he  announced, 
he    certainly   calculated   it  rightly,  as    we  find  by  comparison    with 
Mr.  Shanks.' 

There  is  a  point  about  Mr.  Shanks'  608  figures  of  the  value 
of  TT  which  attracts  attention,  perhaps  without  deserving  it.  It 
might  be  expected  that,  in  so  many  figures,  the  nine  digits  and 
the  cipher  would  occur  each  about  the  same  number  of  times ; 
that  iSj  each  about  61  times.  But  the  fact  stands  thus  :  3  occurs 
68  times ;  9  and  2  occur  67  times  each  ;  4  occurs  64  times ;  1 
and  6  occur  62  times  each;  0  occurs  60  times;  8  occurs  58  times; 

5  occurs  56  times  ;  and  7  occurs  only  44  times.     Now,  if  all  the 
digits  were  equally  likely,  and  608  drawings  were  made,  it  is  45 
to    1  against  the  number  of  sevens  being  as  distant  from  the 
probable  average  (say  61)  as  44  on  one  side  or  78  on  the  other. 
There  must  be  some  reason  why  the  number  7  is  thus  deprived  of 
its  fair  share  in  the  structure.     Here  is  a  field  of  speculation  in 
which  two  branches  of  inquirers  might  unite.     There  is  but  one 
number  which  is  treated  with  an  unfairness  which  is  incredible 
as  an  accident  :  and  that  number  is  the  mystic  number  seven  1 


292  A   BUDGET   OF  PARADOXES. 

If  the  cyclometers  and  the  apocalyptics  would  lay  their  heads 
together  until  they  come  to  a  unanimous  verdict  on  this  pheno- 
menon, and  would  publish  nothing  until  they  are  of  one  mind, 
they  would  earn  the  gratitude  of  their  race. — I  was  wrong  :  it  is 
the  Pyramid-speculator  who  should  have  been  appealed  to.  A 
correspondent  of  my  friend  Prof.  Piazzi  Smyth  notices  that  3  is 
the  number  of  most  frequency,  and  that  3^-  is  the  nearest  approxi- 
mation to  it  in  simple  digits.  Prof.  Smyth  himself,  whose  word 
on  Egypt  is  paradox  of  a  very  high  order,  backed  by  a  great 
quantity  of  useful  labour,  the  results  of  which  will  be  made 
available  by  those  who  do  not  receive  the  paradoxes,  is  inclined 
to  see  confirmation  for  some  of  his  theory  in  these  phenomena. 

These  parad&xes  of  calculation  sometimes  appear  as  illustrations 
of  the  value  of  a  new  method.  In  1863,  Mr.  G.  Suffield,  M.A. 
and  Mr.  J.  E.  Lunn,  M.A.,  of  Clare  College  and  of  St.  John's 
College,  Cambridge,  published  the  whole  quotient  of  10000  .  .  . 
divided  by  7699,  throughout  the  whole  of  one  of  the  recurring 
periods,  having  7698  digits.  This  was  done  in  illustration  of 
Mr.  Suffield's  method  of  Synthetic  division. 

Another  instance  of  computation  carried  paradoxical  length,  in 
order  to  illustrate  a  method,  is  the  solution  of  a?3  — 2#  =  5,  the 
example  given  of  Newton's  method,  on  which  all  improvements 
have  been  tested.  In  1831,  Fourier's  posthumous  work  on  equa- 
tions showed  33  figures  of  solution,  got  with  enormous  labour. 
Thinking  this  a  good  opportunity  to  illustrate  the  superiority  of 
the  method  of  W.  Gr.  Homer,  not  then  known  in  France,  and 
not  much  known  in  England,  I  proposed  to  one  of  my  classes,  in 
1841,  to  beat  Fourier  on  this  point,  as  a  Christmas  exercise.  I 
received  several  answers,  agreeing  with  each  other,  to  50  places 
of  decimals.  In  1848,  I  repeated  the  proposal,  requesting  that 
50  places  might  be  exceeded :  I  obtained  answers  of  75,  65,  63, 
58,  57,  and  52  places.  But  one  answer,  by  Mr.  W.  Harris  John- 
ston, of  Dundalk,  and  of  the  Excise  Office,  went  to  101  decimal 
places.  To  test  the  accuracy  of  this,  I  requested  Mr.  Johnston  to 
undertake  another  equation,  connected  with  the  former  one  in  a 
way  which  I  did  not  explain.  His  solution  verified  the  former 
one,  but  he  was  unable  to  see  the  connexion,  even  when  his 
result  was  obtained.  My  reader  may  be  as  much  at  a  loss  :  the 
two  solutions  are — 

2-0945514815423265  .  .  . 

9-0544851845767340  .  .  . 

The  results  are  published  in  the  Mathematician,  vol.  iii.  p.  290. 


HORNER'S  METHOD-COMETS.  293 

In  1851,  another  pupil  of  mine,  Mr.  J.  Power  Hicks,  carried  the 
result  to  152  decimal  places,  without  knowing  what  Mr.  Johnston 
had  done.  The  result  is  in  the  English  Cyclopcedia,  article 
INVOLUTION  AND  EVOLUTION. 

I  remark  that  when  I  write  the  initial  of  a  Christian  name,  the 
most  usual  name  of  that  initial  is  understood.  I  never  saw  the 
name  of  W.  Gr.  Horner  written  at  length,  until  I  applied  to  a 
relative  of  his,  who  told  me  that  he  was,  as  I  supposed,  Wm. 
George,  but  that  he  was  named  after  a  relative  of  that  surname. 

The  square  root  of  2,  to  110  decimal  places,  was  given  me  in 
1852  by  my  pupil,  Mr.  William  Henry  Colvill,  now  (1867)  Civil 
Surgeon  at  Baghdad.  It  was 

1-4142135623730950488016887242096980785696 
7187537694807317667973799073247846210703 
885038753432  764157273501384623 

Mr.  James  Steel  of  Birkenhead  verified  thia  by  actual  multipli- 
cation, and  produced 

2  _  2580413 

1011? 
as  the  square. 

Calcolo  decidozzinale  del  Barone  Silvio  Ferrari.    Turin,  1854,  4to. 

This  is  a  serious  proposal  to  alter  our  numeral  system  and  to 
count  by  twelves.  Thus  10  would  be  twelve,  11  thirteen,  &c., 
two  new  symbols  being  invented  for  ten  and  eleven.  The  names 
of  numbers  must  of  course  be  changed.  There  are  persons  who 
think  such  changes  practicable.  I  thought  this  proposal  absurd 
when  I  first  saw  it,  and  I  think  so  still :  but  the  one  I  shall 
presently  describe  beats  it  so  completely  in  that  point,  that  I 
have  not  a  smile  left  for  this  one. 


The    successful  and  thei'efore  probably  true    theory  of   Comets. 
London,  1854.     (4  pp.  duodecimo.) 

The  author  is  the  late  Mr.  Peter  Legh,  of  Norbury  Booths 
Hall,  Knutsford,  who  published  for  eight  or  ten  years  the  Ombro- 
logical  Almanac,  a  work  of  asserted  discovery  in  meteorology. 
The  theory  of  comets  is  that  the  joint  attraction  of  the  new 
moon  and  several  planets  in  the  direction  of  the  sun,  draws  off 
the  gases  from  the  earth,  and  forms  these  cometic  meteors.  But 
how  these  meteors  come  to  describe  orbits  round  the  sun,  and  to 


204  A  BUDGET   OF  PARADOXES. 

become  capable   of  having   their   returns   predicted,   is  not  ex- 
plained. 

The  Mormon,  New  York,  Saturday,  Oct.  27,  1855. 

A  newspaper  headed  by  a  grand  picture  of  starred  and  striped 
banners,  beehive,  and  eagle  surmounting  it.  A  scroll  on  each 
side :  on  the  left,  '  Mormon  creed.  Mind  your  own  business. 
Brigham  Young ; '  on  the  right,  '  Given  by  inspiration  of  Grod. 
Joseph  Smith.'  A  leading  article  on  the  discoveries  of  Prof. 
Orson  Pratt  says,  'Mormonism  has  long  taken  the  lead  in  religion: 
it  will  soon  be  in  the  van  both  in  science  and  politics.'  At  the 
beginning  of  the  paper  is  Prof.  Pratt's  '  Law  of  Planetary  Rota- 
tion.' The  cube  roots  of  the  densities  of  the  planets  are  as  the 
square  roots  of  their  periods  of  rotation.  The  squares  of  the  cube 
roots  of  the  masses  divided  by  the  squares  of  the  diameters  are 
as  the  periods  of  rotation.  Arithmetical  verification  attempted, 
and  the  whole  very  modestly  stated  and  commented  on.  Dated 
Gr.  S.  L.  City,  Utah  Ter.,  Aug.  1,  1855.  If  the  creed,  as  above, 
be  correctly  given,  no  wonder  the  Mormonites  are  in  such  bad 
odour. 

The   two   estates ;    or  both   worlds    mathematically   considered. 
London,  1855,  small  (pp.  16). 

The  author  has  published  mathematical  works  with  his  name. 
The  present  tract  is  intended  to  illustrate  mathematically  a  point 
which  may  be  guessed  from  the  title.  But  the  symbols  do  very 
little  in  the  way  of  illustration  :  thus,  x  being  the  present  value 
of  the  future  estate  (eternal  happiness),  and  a  of  all  that  this 
world  can  give,  the  author  impresses  it  on  the  mathematician 
that,  x  being  infinitely  greater  than  a,  x  +  a—x,  so  that  a  need 
not  be  considered.  This  will  not  act  much  more  powerfully  on 
a  mathematician  by  virtue  of  the  symbols  than  if  those  same 
symbols  had  been  dispensed  with :  even  though,  as  the  author 
adds,  '  It  was  this  method  of  neglecting  infinitely  small  quantities 
that  Sir  Isaac  Newton  was  indebted  to  for  his  greatest  discoveries.' 

There  has  been  a  moderate  quantity  of  well-meant  attempt  to 
enforce,  sometimes  motive,  sometimes  doctrine,  by  arguments 
drawn  from  mathematics,  the  proponents  being  persons  unskilled 
in  that  science  for  the  most  part.  The  ground  is  very  dangerous : 
for  the  illustration  often  turns  the  other  way  with  greater  power, 
in  a  manner  which  requires  only  a  little  more  knowledge  to  see. 


MATHEMATICAL   ILLUSTRATIONS   OF   DOCTRINE.  295 

I  have,  in  my  life,  heard  from  the  pulpit  or  read,  at  least  a  dozen 
times,  that  all  sin  is  infinitely  great,  proved  as  follows.  The 
greater  the  being,  the  greater  the  sin  of  any  offence  against  him : 
therefore  the  offence  committed  against  an  infinite  being  is 
infinitely  great.  Now  the  mathematician,  of  which  the  proposers 
of  this  argument  are  not  aware,  is  perfectly  familiar  with 
quantities  which  increase  together,  and  never  cease  increasing, 
but  so  that  one  of  them  remains  finite  when  the  other  becomes 
infinite.  In  fact,  the  argument  is  a  perfect  non  sequitur.  Those 
who  propose  it  have  in  their  minds,  though  in  a  cloudy  and  in- 
definite form,  the  idea  of  the  increase  of  guilt  being  propor- 
tionate to  the  increase  of  greatness  in  the  being  offended.  But 
this  it  would  never  do  to  state  :  for  by  such  statement  not  only 
would  the  argument  lose  all  that  it  has  of  the  picturesque,  but 
the  asserted  premise  would  have  no  strong  air  of  exact  truth. 
How  could  any  one  undertake  to  appeal  to  conscience  to  declare 
that  an  offence  against  a  being  4-j-7^-  times  as  great  as  another  is 
exactly,  no  more  and  no  less,  4T7^-  times  as  great  an  offence  against 
the  other  ? 

The  infinite  character  of  the  offence  against  an  infinite  being 
is  laid  down  in  Dryden's  Religio  Laid,  and  is,  no  doubt,  an  old 
argument : — 

For,  granting  we  have  sinned,  and  that  th'  offence 

Of  man  is  made  against  Omnipotence, 

Some  price  that  bears  proportion  must  be  paid, 

And  infinite  with  infinite  be  weighed. 

See  then  the  Deist  lost ;  remorse  for  vice 

Not  paid  ;  or,  paid,  inadequate  in  price. 

Dryden,  in  the  words  '  bears  proportion '  is  in  verse  more 
accurate  than  most  of  the  recent  repeaters  in  prose,  And  this  is 
not  the  only  case  of  the  kind  in  his  argumentative  poetry. 

My  old  friend,  the  late  Dr.  Olinthus  Gregory,  who  was  a  sound 
and  learned  mathematician,  adopted  this  dangerous  kind  of 
illustration  in  his  Letters  on  the  Christian  Eeligion.  He  argued, 
by  parallel,  from  what  he  supposed  to  be  the  necessarily  mysterious 
nature  of  the  impossible  quantity  of  algebra  to  the  necessarily 
mysterious  nature  of  certain  doctrines  of  his  system  of  Chris- 
tianity. But  all  the  difficulty  and  mystery  of  the  impossible 
quantity  is  now  cleared  away  by  the  advance  of  algebraical 
thought :  and  yet  Dr.  Gregory's  book  continues  to  be  sold,  and 
no  doubt  the  illustration  is  still  accepted  as  appropriate. 

The  mode  of  argument  used  by  the  author  of  the  tract  above 


296  A  BUDGET   OF  PARADOXES. 

named  has  a  striking  defect.  He  talks  of  reducing  this  world 
and  the  next  to  '  present  value,'  as  an  actuary  does  with  succes- 
sive lives  or  next  presentations.  Does  value  make  interest  ?  and 
if  not,  why  ?  And  if  it  do,  then  the  present  value  of  an  eternity 
is  not  infinitely  great.  Who  is  ignorant  that  a  perpetual  annuity 
at  five  per  cent,  is  worth  only  twenty  years'  purchase  ?  This 
point  ought  to  be  discussed  by  a  person  who  treats  heaven  as  a 
deferred  perpetual  annuity.  I  do  not  ask  him  to  do  so,  and 
would  rather  he  did  not ;  but  if  he  will  do  it,  he  must  either 
deal  with  the  question  of  discount,  or  be  asked  the  reason  why. 

When  a  very  young  man,  I  was  frequently  exhorted  to  one  or 
another  view  of  religion  by  pastors  and  others  who  thought  that 
a  mathematical  argument  would  be  irresistible.  And  I  heard  the 
following  more  than  once,  and  have  since  seen  it  in  print,  I  forget 
where.  Since  eternal  happiness  belonged  to  the  particular  views 
in  question,  a  benefit  infinitely  great,  then,  even  if  the  probability 
of  their  arguments  were  small,  or  even  infinitely  small,  yet  the 
product  of  the  chance  and  benefit,  according  to  the  usual  rule, 
might  give  a  result  which  no  one  ought  in  prudence  to  pass  over. 
They  did  not  see  that  this  applied  to  all  systems  as  well  as  their 
own.  I  take  this  argument  to  be  the  most  perverse  of  all  the 
perversions  I  have  heard  or  read  on  the  subject :  there  is  some 
high  authority  for  it,  whom  I  forget. 

The  moral  of  all  this  is,  that  such  things  as  the  preceding 
should  be  kept  out  of  the  way  of  those  who  are  not  mathe- 
maticians, because  they  do  not  understand  the  argument ;  and  of 
those  who  are,  because  they  do. 

[The  high  authority  referred  to  above  is  Pascal,  an 
early  cultivator  of  mathematical  probability,  and  obviously  too 
much  enamoured  of  his  new  pursuit.  But  he  conceives  himself 
bound  to  wager  on  one  side  or  the  other.  To  the  argument 
(Pensees,  ch.  7)  that  '  le  juste  est  de  ne  point  parier,'  he  answers, 
'  Oui :  mais  il  faut  parier :  vous  6tes  embarque ;  et  ne  parier 
point  que  Dieu  est,  c'est  parier  qu'il  n'est  pas.'  Leaving  Pascal's 
argument  to  make  its  way  with  a  person  who,  being  a  sceptic,  is 
yet  positive  that  the  issue  is  salvation  or  perdition,  if  a  Grod  there 
be, — for  the  case  as  put  by  Pascal  requires  this, — I  shall  merely 
observe  that  a  person  who  elects  to  believe  in  Grod,  as  the  best 
chance  of  gain,  is  not  one  who,  according  to  Pascal's  creed,  or 
any  other  worth  naming,  will  really  secure  that  gain;  I  wonder 
whether  Pascal's  curious  imagination  ever  presented  to  him  in 
sleep  his  convert,  in  the  future  state,  shaken  out  of  a  red-hot 
dice-box  upon  a  red-hot  hazard»table,  as  perhaps  he  might  have 


XOVUM  OBGANOI  MORALIUM.  297 

been,  if  Dante  had  been  the  later  of  the  two.  The  original  idea 
is  due  to  the  elder  Arnobius,  who,  as  cited  by  Bayle,  speaks 
thus: — 

'  Sed  et  ipse  [Christus]  quse  pollicetur,  non  probat.  Ita  est.  Xulla 
enim,  ut  dixi,  futnrorum  potest  existere  comprobatio.  Cum  ergo  haec 
sit  conditio  rntnroruni,  ut  teneri  et  comprehend!  nnllius  possint 
anticipationis  attactu  ;  nonne  purior  ratio  est,  ex  duobus  incertis,  et  in 
ambigua  expectatione  pendentibus,  id  potius  credere,  quod  aliqnas 
spes  ferat,  quam  omnino  quod  nnllas  ?  In  illo  enim  periculi  nihil  est, 
si  quod  dicitur  imminere,  cassnm  fiat  et  vacuum  :  in  hoc  damnum 
est  maximum,  id  est  salutis  amissio,  si  cum  tempus  advenerit  aperiatur 
non  faisse  mendacium.' 

Really  Arnobius  seems  to  have  got  as  much  out  of  the  notion, 
in  the  third  century,  as  if  he  had  been  fourteen  centuries  later, 
with  the  arithmetic  of  chances  to  help  him.] 

The  Sentinel,  vol.  ix.  no.  27.     London,  Saturday,  May  26,  1855. 

This  is  the  first  London  number  of  an  Irish  paper,  Protestant 
in  politics.  It  opens  with  '  Suggestions  on  the  subject  of  a  3*t"-</  m 
Organum  Moralium^  which  is  the  application  of  algebra  and  the 
differential  calculus  to  morals,  socials,  and  politics.  There  is  also  a 
leading  article  on  the  subject,  and  some  applications  in  notes  to 
other  articles.  A  separate  publication  was  afterwards  made,  with 
the  addition  of  a  long  Preface  ;  the  author  being  a  clergyman  who 
I  presume  must  have  been  the  editor  of  the  Sentinel. 

Suggestions  as  to  the  employment  of  a  Novum  Organum  Mora- 
Hum.  Or,  thoughts  on  the  nature  of  the  Differential  Calculus, 
and  on  the  application  of  its  principles  to  metaphysics,  with  a 
view  to  the  attainment  of  demonstration  and  certainty  in  moral, 
political  and  ecclesiastical  affairs.  By  Tresham  Dames  Gregg, 
Chaplain  of  St.  Mary's,  within  the  church  of  St.  Nicholas  intra 
mnros,  Dublin.  London  1859,  8vo.  (pp.  xl  +  32). 

I  have  a  personal  interest  in  this  system,  as  will  appear  from 
the  following  extract  from  the  newspaper  : — 

'  "We  were  subsequently  referred  to  De  Morgan's  "  Formal  Logic  " 
and  Boole's  "  Laws  of  Thought,"  both  very  elaborate  works,  and 
greatly  in  the  direction  taken  by  ourselves.  That  the  writers  amazingly 
surpass  us  in  learning  we  most  willingly  admit,  but  we  venture  to 
pronounce  of  both  their  learned  treatises,  that  they  deal  with  the 
subject  in  a  mode  that  is  scholastic  to  an  excess  .  .  .  That  their  works 
have  been  for  a  considerable  space  of  time  before  the  world  and 


298  A  BUDGET  OF  PARADOXES. 

effected  nothing,  would  argue  that  they  have  overlooked  the  vital 
nature  of  the  theme.  .  .  On  the  whole,  the  writings  of  De  Morgan  and 
Boole  go  to  the  full  justification  of  our  principle  without  in  any  wise 
so  trenching  upon  our  ground  as  to  render  us  open  to  reproach  in 
claiming  our  Calculus  as  a  great  discovery.  .  .  But  we  renounce  any 
paltry  jealousy  as  to  a  matter  so  vast.  If  De  Morgan  and  Boole  have 
had  a  priority  in  the  case,  to  them  we  cheerfully  shall  resign  the  glory 
and  honour.  If  such  be  the  truth,  they  have  neither  done  justice  to 
the  discovery,  nor  to  themselves  [quite  true].  They  have,  under  the 
circumstances,  acted  like  '  the  foolish  man,  who  roasteth  not  that 
which  he  taketh  in  hunting.'  .  .  It  will  be  sufficient  for  us,  however,  to 
be  the  Columbus  of  these  great  Americi,  and  popularise  what  they 
found,  if  they  found  it.  We,  as  from  the  mountain  top,  will  then 
become  their  trumpeters,  and  cry  glory  to  De  Morgan  and  glory  to 
Boole,  under  Him  who  is  the  source  of  all  glory,  the  only  good  and 
wise,  to  Whom  be  glory  for  ever !  If  they  be  our  predecessors  in 
this  matter,  they  have,  under  Him,  taken  moral  questions  out  of  the 
category  of  probabilities,  and  rendered  them  perfectly  certain.  In  that 
case,  let  their  books  be  read  by  those  who  may  doubt  the  principles  this 
day  laid  before  the  world  as  a  great  discovery,  by  our  newspaper. 
Our  cry  shall  be  tvprjKaai  \  Let  us  hope  that  they  will  join  us,  and 
henceforth  keep  their  right  [sic]  from  under  their  bushel.' 

For  myself,  and  for  my  old  friend  Mr.  Boole,  who  I  am  sure 
would  join  me,  I  disclaim  both  priority,  simultaneity,  and 
posteriority,  and  request  that  nothing  may  be  trumpeted  from 
the  mountain  top  except  our  abjuration  of  all  community  of 
thought  or  operation  with  this  Novum  Organum. 

To  such  community  we  can  make  no  more  claim  than  Americus 
could  make  to  being  the  forerunner  of  Columbus  who  popularised 
his  discoveries.  We  do  not  wish  for  any  svprjicao-i,  and  not  even  for 
svprjKaa-i.  For  self  and  Boole,  I  point  out  what  would  have  con- 
vinced either  of  us  that  this  house  is  divided  against  itself. 
.  A  being  the  apostolic  element,  8  the  doctrinal  element,  and 
X  the  body  of  the  faithful,  the  church  is  A  8  X,  we  are  told. 
Also,  that  if  A  become  negative,  or  the  Apostolicity  become 
Diabolicity  [my  words] ;  or  if  8  become  negative,  and  doctrine 
become  heresy ;  or  if  X  become  negative,  that  is,  if  the  faithful 
become  unfaithful ;  the  church  becomes  negative,  *  the  very 
opposite  of  what  it  ought  to  be.'  For  self  and  Boole,  I  admit 
this.  But — which  is  not  noticed — if  A  and  8  should  both  become 
negative,  diabolical  origin  and  heretical  doctrine,  then  the  church, 
A  8  X,  is  still  positive,  what  it  ought  to  be,  unless  X  be  also 
negative,  or  the  people  unfaithful  to  it,  in  which  case  it  is  a  bad 
church.  Now,  self  and  Boole — though  I  admit  I  have  not  asked 


DE  MORGAN  AND  BOOLE  CORRECTED.  299 

my  partner — are  of  opinion  that  a  diabolical  church  with  falsfe 
doctrine  does  harm  when  the  people  are  faithful,  and  can  do 
good  only  when  the  people  are  unfaithful.  We  may  be  wrong^ 
but  this  is  what  we  do  think.  Accordingly,  we  have  caught 
nothing,  and  can  therefore  roast  nothing  of  our  own :  I  content 
myself  with  roasting  a  joint  of  Mr.  Gregg's  larder. 

These  mathematical  vagaries  have  uses  which  will  justify  a 
large  amount  of  quotation :  and  in  a  score  of  years  this  may 
perhaps  be  the  only  attainable  record.  I  therefore  proceed. 

After  observing  that  by  this  calculus  juries  (heaven  help  them  I 
say  I)  can  calculate  damages  '  almost  to  a  nicety,'  and  further 
that  it  is  made  abundantly  evident  that  c  e  x  is  '  the  general 
expression  for  an  individual,'  it  is  noted  that  the  number  of  the 
Beast  is  not  given  in  the  Revelation  in  words  at  length,  but  as 
X&  •  On  this  the  following  remark  is  made  : — 

'  Can  it  be  possible  that  we  have  in  this  case  a  specimen  given  to  us 
of  the  arithmetic  of  heaven,  and  an  expression  revealed,  which  indicates 
by  its  function  of  addibility,  the  name  of  the  church  in  question,  and 
of  each  member  of  it ;  and  by  its  function  of  multiplicability  the 
doctrine,  the  mission,  and  the  members  of  the  great  Synagogue  of 
Apostacy  ?  We  merely  propound  these  questions  ; — we  do  not  pretend 
to  solve  them.' 

After  a  translation  in  blank  verse  —a  very  pretty  one-  -of  the 
18th  Psalm,  the  author  proceeds  as  follows,  to  render  it  into 
differential  calculus : — 

'  And  the  whole  tells  us  just  this,  that  David  did  what  he  could.  He 
augmented  those  elements  of  his  constitution  which  were  (exceptis 
excipiendis)  subject  to  himself,  and  the  Almighty  then  augmented  his 
personal  qualities,  and  his  vocational  status.  Otherwise,  to  throw  the 
matter  into  the  expression  of  our  notation,  the  variable  e  was  aug- 
mented, and  c  x  rose  proportionally.  The  law  of  the  variation,  accord- 
ing to  our  theory,  would  be  thus  expressed.  The  resultant  was  David 
the  king  c  e  x  [c=r?]  (who  had  been  David  the  shepherd  boy),  and 
from  the  conditions  of  the  theorem  we  have 

- du  dx   .          dc 

_   =  c  e  - — \-ex-      x  +  c  x 
de  de  de 

which,  in  the  terms  of  ordinary  language,  just  means,  the  increase  of 
David's  educational  excellence  or  qualities — his  piety,  his  prayerfulness, 
his  humility,  obedience,  &c. — was  so  great,  that  when  multiplied  by  his 
original  talent  and  position,  it  produced  a  product  so  great  as  to  be 
equal  in  its  amount  to  royalty,  honour,  wealth,  and  power,  &c.  :  in 
short,  to  all  the  attributes  of  majesty.' 

The  '  solution  of  the  family  problem '  is  of  high  interest.     It  is 


300  A  BUDGET  OF  PARADOXES. 

to  determine  the  effect  on  the  family  in  general  from  a  change 
[of  conduct]  in  one  of  them.  The  person  chosen  is  one  of  the 
maid-servants. 

'  Let  c  e  a  be  the  father ;  CiC]Xl  the  mother,  &c.  The  family  then 
consists  of  the  maid's  master,  her  mistress,  her  young  master,  her 
young  mistress,  and  fellow  servant.  Now  the  master's  calling  (or  c) 
is  to  exercise  his  share  of  control  over  this  servant,  and  mind  the  rest 
of  his  business  :  call  this  remainder  a,  and  let  his  calling  generally,  or 

all  his  affairs,  be  to  his  maid-servant  as  m  :  y,  i.  e.,  y  =        ; .  .  .  .  and 

c 

this  expression  will  represent  his  relation  to  the  servant.    Consequently, 

(i    mz\  ,-,         .       /      ,     mz\ 

a  +  -      }  e  x ;  otherwise  (  a  +  —   ]  e  x 
c  )  \  c  / 

is  the  expression  for  the  father  when  viewed  as  the  girl's  master.' 

I  have  no  objection  to  repeat  so  far;  but  I  will  not  give  the 
formula  for  the  maid's  relation  to  her  young  master ;  for  I  am 
not  quite  sure  that  all  young  masters  are  to  be  trusted  with  it. 
Suffice  it  that  the  son  will  be  affected  directly  as  his  influence 
over  her,  and  inversely  as  his  vocational  power  :  if  then  he  should 
have  some  influence  and  no  vocational  power,  the  effect  on  him 
would  be  infinite.  This  is  dismal  to  think  of.  Further,  the 
formula  brings  out  that  if  one  servant  improve,  the  other  must 
deteriorate,  and  vice  versa.  This  is  not  the  experience  of  most 
families  :  and  the  author  remarks  as  follows : — 

'  That  is,  we  should  venture  to  say,  a  very  beautiful  result,  and  we 
may  say  it  yielded  us  no  little  astonishment.  What  our  calculation 
might  lead  to  we  never  dreamt  of ;  that  it  should  educe  a  conclusion 
so  recondite  that  our  unassisted  power  never  could  have  attained  to, 
and  which,  if  we  could  have  conjectured  it,  would  have  been  at  best 
the  most  distant  probability,  that  conclusion  being  itself,  as  it  would 
appear,  the  quintessence  of  truth,  afforded  us  a  measure  of  satisfaction 
that  was  not  slight.' 

That  the  writings  of  Mr.  Boole  and  myself  '  go  to  the  full 
justification  of  this  '  principle,'  is  only  true  in  the  sense  in  which 
the  Scotch  use,  or  did  use,  the  word  justification. 

[The  last  number  of  this  Budget  had  stood  in  type  for  months, 
waiting  until  there  should  be  a  little  cessation  of  correspondence 
more  connected  with  the  things  of  the  day.  I  had  quite  for- 
gotten what  it  was  to  contain ;  and  little  thought,  when  I  read 
the  proof,  that  my  allusions  to  my  friend  Mr.  Boole,  then  in  life 
and  health,  would  not  be  printed  till  many  weeks  after  his  death. 
Had  I  remembered  what  my  last  number  contained,  I  should  have 


BOOLE'S  LAWS   OF  THOUGHT.  301 

added  my  expression  of  regret  and  admiration  to  the  numerous 
obituary  testimonials,  which  this  great  loss  to  science  has  called 
forth. 

The  system  of  logic  alluded  to  in  the  last  number  of  this  series 
is  but  one  of  many  proofs  of  genius  and  patience  combined.  I 
might  legitimately  have  entered  it  among  my  paradoxes,  or 
things  counter  to  general  opinion  :  but  it  is  a  paradox  which,  like 
that  of  Copernicus,  excited  admiration  from  its  first  appearance. 
That  the  symbolic  processes  of  algebra,  invented  as  tools  of 
numerical  calculation,  should  be  competent  to  express  every  act 
of  thought,  and  to  furnish  the  grammar  and  dictionary  of  an  all- 
containing  system  of  logic,  would  not  have  been  believed  until  it 
was  proved.  When  Hobbes,  in  the  time  of  the  Commonwealth, 
published  his  '  Computation  or  Logique,'  he  had  a  remote  glimpse 
of  some  of  the  points  which  are  placed  in  the  light  of  day  by  Mr. 
Boole.  The  unity  of  the  forms  of  thought  in  all  the  applications 
of  reason,  however  remotely  separated,  will  one  day  be  matter 
of  notoriety  and  common  wonder  :  and  Boole's  name  will  be  re- 
membered in  connexion  with  one  of  the  most  important  steps 
towards  the  attainment  of  this  knowledge.] 

The  Decimal  System  as  a  whole.    By  Dover  Statter.    London  and 

Liverpool,  1856,  8vo. 

The  proposition  is  to  make  everything  decimal.  The  day,  now 
24  hours,  is  to  be  made  10  hours.  The  year  is  to  have  ten  months, 
Unusber,  Duober,  &c.  Fortunately  there  are  ten  commandments, 
so  there  will  be  neither  addition  to,  nor  deduction  from,  the 
moral  law.  But  the  twelve  apostles  I  Even  rej  ecting  Judas, 
there  is  a  whole  apostle  of  difficulty.  These  points  the  author 
does  not  touch. 

The  first  book  of  Phonetic  Reading.  London,  Fred.  Pitman, 
Phonetic  Depot,  20,  Paternoster  Bow,  1856,  12mo. 

The  Phonetic  Journal.  Devoted  to  the  propagation  of  phonetic 
reading,  phonetic .  longh and,  phonetic  shorthand,  and  phonetic 
printing.  No.  46.  Saturday,  15  November  1856.  Vol.  15. 

I  write  the  titles  of  a  couple  out  of  several  tracts  which  I 
have  by  me.  But  the  number  of  publications  issued  by  the  pro- 
moters of  this  spirited  attempt  is  very  large  indeed.  The  attempt 
itself  has  had  no  success  with  the  mass  of  the  public.  This  I  do 
not  regret.  Had- the  world  found  that  the  change  was  useful,  I 
should  have  gone  contentedly  with  the  stream  ;  but  not  without 
regretting  our  old  language.  I  admit  the  difficulties  which  our 


302  A  BUDGET  OF  PAKADOXES. 

unpronouncable  spelling  puts  in  the  way  of  learning  to  read :  and 
I  have  no  doubt  that,  as  affirmed,  it  is  easier  to  teach  children 
phonetically,  and  afterwards  to  introduce  them  to  our  common 
system,  than  to  proceed  in  the  usual  way.  But  by  the  usual  way 
I  mean  proceeding  by  letters  from  the  very  beginning.  If,  which 
I  am  sure  is  a  better  plan,  children  be  taught  at  the  commence- 
ment very  much  by  complete  words,  as  if  they  were  learning 
Chinese,  and  be  gradually  accustomed  to  resolve  the  known  words 
into  letters,  a  fraction,  perhaps  a  considerable  one,  of  the  advan- 
tage of  the  phonetic  system  is  destroyed.  It  must  be  remem- 
bered that  a  phonetic  system  can  only  be  an  approximation.  The 
differences  of  pronunciation  existing  among  educated  persons 
are  so  great,  that,  on  the  phonetic  system,  different  persons  ought 
to  spell  differently. 

But  the  phonetic  party  have  produced  something  which  will 
immortalize  their  plan  :  I  mean  their  shorthand,  which  has  had 
a  fraction  of  the  success  it  deserves.  All  who  know  anything  of 
shorthand  must  see  that  nothing  but  a  phonetic  system  can  be 
worthy  of  the  name  :  and  the  system  promulgated  is  skilfully 
done.  Were  I  a  young  man  I  should  apply  myself  to  it  syste- 
matically. I  believe  this  is  the  only  system  in  which  books  were 
ever  published.  I  wish  some  one  would  contribute  to  a  public 
journal  a  brief  account  of  the  dates  and  circumstances  of  the 
phonetic  movement,  not  forgetting  a  list  of  the  books  published 
in  shorthand. 

A  child  beginning  to  read  by  himself  may  owe  terrible  dreams 
and  waking  images  of  horror  to  our  spelling,  as  I  did  when  six 
years  old.  In  one  of  the  common  poetry-books  there  is  an  ad- 
monition against  confining  little  birds  in  cages,  and  the  child  is 
asked  what  if  a  great  giant,  amazingly  strong,  were  to  take  you 
away,  shut  you  up, 

And  feed  you  with  vic-tu-als  you  ne-ver  could  bear. 

The  book  was  hyphened  for  the  beginner's  use ;  and  I  had  not  the 
least  idea  that  vic-tu-als  were  vittles :  by  the  sound  of  the  word 
I  judged  they  must  be  of  iron ;  and  it  entered  into  my  soul. 

The  worst  of  the  phonetic  shorthand  books  is  that  they  nowhere, 
so  far  as  I  have  seen,  give  all  the  symbols,  in  every  stage  of  ad- 
vancement, together,  in  one  or  following  pages.  It  is  symbols 
and  talk,  more  symbols  and  more  talk,  &c.  A  universal  view  of 
the  signs  ought  to  begin  the  works. 


MAGNITUDE   OF   THE   EARTH— THE   MOON.  303 


Ombrological  Almanac.  Seventeenth  year.  An  essay  on  Anemo- 
logy  and  Ombrology.  By  Peter  Legh,  Esq.  London,  1856, 
12mo. 

Mr.  Legh,  already  mentioned,  was  an  intelligent  country 
gentleman,  and  a  legitimate  speculator.  But  the  clue  was  not 
reserved  for  him. 


The  proof  that  the  three  angles  of  a  triangle  are  equal  to  two 
right  angles  looked  for  in  the  inflation  of  the  circle.  By  Gen. 
Perronet  Thompson.  London,  1856,  8vo.  (pp.  4.) 

Another  attempt,  the  third,  at  this  old  difficulty,  which  cannot 
be  put  into  few  words  of  explanation. 

Comets  considered  as  volcanoes,  and  the  cause  of  their  velocity 
and  other  phenomena  thereby  explained.  London  (circa  1856), 
8vo. 

The  title  explains  the  book  better  than  the  book  explains  the 
title. 

1856.  A  stranger  applied  to  me  to  know  what  the  ideas 
of  a  friend  of  his  were  worth  upon  the  magnitude  of  the  earth. 
The  matter  being  one  involving  points  of  antiquity,  I  mentioned 
various  persons  whose  speculations  he  seemed  to  have  ignored ; 
among  others,  Thales.  The  reply  was,  '  I  am  instructed  by  the 
author  to  inform  you  that  he  is  perfectly  acquainted  with  the 
works  of  Thales,  Euclid,  Archimedes,  .  .  .  '  I  had  some  thought 
of  asking  whether  he  had  used  the  Elzevir  edition  of  Thales, 
which  is  known  to  be  very  incomplete,  or  that  of  Prof.  Niemand 
with  the  lections,  Nirgend,  1824,  2  vols.  folio  ;  just  to  see  whether 
the  last  would  not  have  been  the  very  edition  he  had  read.  But 
I  refrained,  in  mercy. 

The  moon  is  the  image  of  the  Earth,  and  is  not  a  solid  body.  By 
The  Longitude.  (Private  Circulation.)  In  five  parts.  London, 
1856,  1857,  1857 ;  Calcutta,  1858,  1858,  8vo. 

The  earth  is  *  brought  to  a  focus ' ;  it  describes  a  *  looped ' 
orbit  round  the  sun.  The  eclipse  of  the  sun  is  thus  explained  : 
'  At  the  time  of  eclipses,  the  image  is  more  or  less  so  directly 
before  or  behind  the  earth  that,  in  the  case  of  new  moon,  bright 
rays  of  the  sun  fall  and  bear  upon  the  spot  where  the  figure  of 
the  earth  is  brought  to  a  focus,  that  is,  bear  upon  the  image  of 


304  A  BUDGET  OF  PARADOXES. 

the  earth,  when  a  darkness  beyond  is  produced  reaching  to  the 
earth,  and  the  sun  becomes  more  or  less  eclipsed.'  How  the 
earth  is  '  brought  to  a  focus '  we  do  not  find  stated.  Writers  of 
this  kind  always  have  the  argument  that  some  things  which  have 
been  ridiculed  at  first  have  been  finally  established.  Those  who 
put  into  the  lottery  had  the  same  kind  of  argument  ;  but  were 
always  answered  by  being  reminded  how  many  blanks  there  were 
to  one  prize.  I  am  loath  to  pronounce  against  anything :  but  it 
does  force  itself  upon  me  that  the  author  of  these  tracts  has 
drawn  a  blank. 

Times,  April  6  or  7,  1856.     The  moon  has  no  rotary  motion. 

A  letter  from  Mr.  Jellinger  Symons,  inspector  of  schools,  which 
commenced  a  controversy  of  many  letters  and  pamphlets.  This 
dispute  comes  on  at  intervals,  and  will  continue  to  do  so.  It 
sometimes  arises  from  inability  to  understand  the  character  of 
simple  rotation,  geometrically;  sometimes  from  not  understanding 
the  mechanical  doctrine  of  rotation. 

Lunar  Motion.  The  whole  argument  stated,  and  illustrated  by 
diagrams ;  with  letters  from  the  Astronomer  Royal.  By 
Jellinger  C.  Symons.  London,  185(3,  8vo. 

The  Astronomer  Koyal  endeavoured  to  disentangle  Mr.  J.  C. 
Symons,  but  failed.  Mr.  Airy  can  correct  the  error  of  a  ship's 
compasses,  because  he  can  put  her  head  which  way  he  pleases  : 
but  this  he  cannot  do  with  a  speculator. 

Mr.  Symons,  in  this  tract,  insinuated  that  the  rotation  of  the 
moon  is  one  of  the  silver  shrines  of  the  craftsmen.  To  see  a 
thing  so  clearly  as  to  be  satisfied  that  all  who  say  they  do  not  see 
it  are  telling  wilful  falsehood,  is  the  nature  of  man.  Many  of  all 
sects  find  much  comfort  in  it,  when  they  think  of  the  others ; 
many  unbelievers  solace  themselves  with  it  against  believers  ; 
priests  of  old  time  founded  the  right  of  persecution  upon  it,  and 
of  our  time,  in  some  cases,  the  right  of  slander  :  many  of  the 
paradoxers  make  it  an  argument  against  students  of  science.  But 
I  must  say  for  men  of  science,  for  the  whole  body,  that  they  are 
fully  persuaded  of  the  honesty  of  the  paradoxers.  The  simple 
truth  is,  that  all  those  I  have  mentioned,  believers,  unbelievers, 
priests,  paradoxers,  are  not  so  sure  they  are  right  in  their  points 
of  difference  that  they  can  safely  allow  themselves  to  be  per- 
suaded of  the  honesty  of  opponents.  Those  who  know  demon- 
stration are  differently  situated.  I  suspect  a  train  might  be  laid 


CAMBRIDGE  DISPUTATIONS.  305 

for  the  formation  of  a  better  habit  in  this  way.  We  know  that 
Suvaroff  taught  his  Eussians  at  Ismail  not  to  fear  the  Turks  by 
accustoming  them  to  charge  bundles  of  faggots  dressed  in 
turbans,  &c. 

At  which  your  wise  men  sneered  in  phrases  witty, 
He  made  no  answer — but  he  took  the  city ! 

Would  it  not  be  a  good  thing  to  exercise  boys,  in  pairs,  in  the 
following  dialogue : — Sir,  you  are  quite  wrong ! — Sir,  I  am  sure 
you  honestly  think  so  !  This  was  suggested  by  what  used  to 

•take  place  at  Cambridge  in  my  day.     By  statute,  every  B.A.  was 
obliged   to  perform  a  certain  number  of  disputations,  and  the 

father  of  the  college  had  to  affirm  that  it  had  been  done.  Some 
were  performed  in  earnest :  the  rest  were  huddled  over  as  follows. 
Two  candidates  occupied  the  places  of  the  respondent  and  the 
opponent :  Recte  statuit  Newtonus,  said  the  respondent :  Recte 
non  statuit  N&wtonus,  said  the  opponent.  This  was  repeated  the 
requisite  number  of  times,  and  counted  for  as  many  acts  and 
opponencies.  The  parties  then  changed  places,  and  each  unsaid 
what  he  had  said  on  the  other  side  of  the  house :  I  remember 
thinking  that  it  was  capital  drill  for  the  House  of  Commons,  if 
any  of  us  should  ever  get  there.  The  process  was  repeated  with 
every  pair  of  candidates. 

The  real  disputations  were  very  severe  exercises.  I  was 
badgered  for  two  hours  with  arguments  given  and  answered  in 
Latin, — or  what  we  called  Latin — against  Newton's  first  section, 
Lagrange's  derived  functions,  and  Locke  on  innate  principles. 
And  though  I  took  off  everything,  and  was  pronounced  by  the 
moderator  to  have  disputed  magno  honore,  I  never  had  such  a 
strain  of  thought  in  my  life.  For  the  inferior  opponents  were 
made  as  sharp  as  their  betters  by  their  tutors,  who  kept  lists  of 
queer  objections,  drawn  from  all  quarters.  The  opponents  used 
to  meet  the  day  before  to  compare  their  arguments,  that  the 
same  might  not  come  twice  over.  But,  after  I  left  Cambridge, 
it  became  the  fashion  to  invite  the  respondent  to  be  present,  who 
therefore  learnt  all  that  was  to  be  brought  against  him.  This 
made  the  whole  thing  a  farce :  and  the  disputations  were 
abolished. 

The  Doctrine  of  the  Moon's  Rotation,  considered  in  a  letter  to  the 
Astronomical  Censor  of  the  Athenceum.  By  Jones  L.  Mac- 
Elshender.  Edinburgh,  1856,  8vo. 

This  is  an  appeal  to  those  cultivated  persons  who  will  read  it 
'  to  overrule  the  dicta  of  judges  who  would  sacrifice-  truth  and 

x 


306  A  BUDGET   OF  PARADOXES. 

justice  to  professional  rule,  or  personal  pique,  pride,  or  prejudice'; 
meaning,  the  great  mass  of  those  who  have  studied  the  subject. 
But  how  ?  Suppose  the  '  cultivated  persons '  were  to  side  with 
the  author,  would  those  who  have  conclusions  to  draw  and 
applications  to  make  consent  to  be  wrong  because  the  '  general 
body  of  intelligent  men,'  who  make  no  special  study  of  the 
subject,  are  against  them  ?  They  would  do  no  such  thing  :  they 
would  request  the  general  body  of  intelligent  men  to  find  their 
own  astronomy,  and  welcome.  But  the  truth  is,  that  this  intelli- 
gent body  knows  better :  and  no  persons  know  better  that  they 
know  better  than  the  speculators  themselves. 

But  suppose  the  general  body  were  to  combine,  in  opposition 
to  those  who  have  studied.  Of  course  all  my  list  must  be  admit- 
ted to  their  trial ;  and  then  arises  the  question  whether  both 
sides  are  to  be  heard.  If  so,  the  general  body  of  the  intelligent 
must  hear  all  the  established  side  have  to  say :  that  is,  they  must 
become  just  as  much  of  students  as  the  inculpated  orthodox 
themselves.  And  will  they  not  then  get  into  professional  rule, 
pique,  pride,  and  prejudice,  as  the  others  did  ?  But  if,  which  I 
suspect,  they  are  intended  to  judge  just  as  they  are,  they  will  be 
in  a  rare  difficulty.  All  the  paradoxers  are  of  like  pretensions : 
they  cannot,  as  a  class,  be  right,  for  each  one  contradicts  a  great 
many  of  the  rest.  There  will  be  the  puzzle  which  silenced  the 
crew  of  the  cutter  in  Marryat's  novel  of  the  Dog  Fiend.  '  A  tog 
is  a  tog,'  said  Jansen. — '  Yes,'  replied  another,  '  we  all  know  a 
dog  is  a  dog ;  but  the  question  is — Is  this  dog  a  dog  ? '  And  this 
qiiestion  would  arise  upon  every  dog  of  them  all. 

Zetetic  Astronomy :  Earth  not  a  globe.     1857  (Broadsheet). 

Though  only  a  travelling  lecturer's  advertisement,  there  are 
so  many  arguments  and  quotations  that  it  is  a  little  pamphlet. 
The  lecturer  gained  great  praise  from  provincial  newspapers  for 
his  ingenuity  in  proving  that  the  earth  is  a  flat,  surrounded  by 
ice.  Some  of  the  journals  rather  incline  to  the  view :  but  the 
Leicester  Advertiser  thinks  that  the  statements  'would  seem 
very  seriously  to  invalidate  some  of  the  most  important  conclu- 
sions of  modern  astronomy,'  while  the  Norfolk  Herald  is  clear 
that  'there  must  be  a  great  error  on  one  side  or  the  other.'  This 
broadsheet  is  printed  at  Aylesbury  in  1857,  and  the  lecturer  calls 
himself  Parallax:  but  at  Trowbridge,  in  1849,  he  was  S.  Goulden. 
In  this  last  advertisement  is  the  following  announcement : — '  A 
paper  on  the  above  subjects  was  read  before  the  Council  and 


ZETETIC   ASTRONOMY.  307 

Members  of  the  Royal  Astronomical  Society,  Somerset  House, 
Strand,  London  (Sir  John  F.  W.  Herschel,  President),  Friday, 
Dec.  8,  1848.'  No  account  of  such  a  paper  appears  in  the  Notice 
for  that  month  :  I  suspect  that  the  above  is  Mr.  S.  Groulden's 
way  of  representing  the  following  occurrence  : — Dec.  8,  1 848,  the 
Secretary  of  the  Astronomical  Society  (De  Morgan  by  name)  said, 
at  the  close  of  the  proceedings, — '  Now,  gentlemen,  if  you  will 
promise  not  to  tell  the  Council,  I  will  read  something  for  your 
amusement ' :  and  he  then  read  a  few  of  the  arguments  which 
had  been  transmitted  by  the  lecturer.  The  fact  is  worth  noting 
that  from  1849  to  1857,  arguments  on  the  roundness  or  flatness 
of  the  earth  did  itinerate.  I  have  no  doubt  they  did  much  good: 
for  very  few  persons  have  any  distinct  idea  of  the  evidence  for  the 
rotundity  of  the  earth.  The  Blackburn  Standard  and  Preston 
Guardian  (Dec.  12  and  16,  1849)  unite  in  stating  that  the 
lecturer  ran  away  from  his  second  lecture  at  Burnley,  having  been 
rather  too  hard  pressed  at  the  end  of  his  first  lecture  to  explain 
why  the  large  hull  of  a  ship  disappeared  before  the  sails.  The 
persons  present  and  waiting  for  the  second  lecture  assuaged  their 
disappointment  by  concluding  that  the  lecturer  had  slipped  off 
the  icy  edge  of  his  flat  disk,  and  that  he  would  not  be  seen  again 
till  he  peeped  up  on  the  opposite  side. 

But,  strange  as  it  may  appear,  the  opposer  of  the  earth's  round- 
ness has  more  of  a  case — or  less  of  a  want  of  case — than  the 
arithmetical  squarer  of  the  circle.  The  evidence  that  the  earth 
is  round  is  but  cumulative  and  circumstantial :  scores  of  pheno- 
mena ask,  separately  and  independently,  what  other  explanation 
can  be  imagined  except  the  sphericity  of  the  earth.  The  evidence 
for  the  earth's  figure  is  tremendously  powerful  of  its  kind ;  but 
the  proof  that  the  circumference  is  3-14159265  .  .  .  times  the 
diameter  is  of  a  higher  kind,  being  absolute  mathematical 
demonstration. 

The  Zetetic  system  still  lives  in  lectures  and  books ;  as  it 
ought  to  do,  for  there  is  no  way  of  teaching  a  truth  comparable 
to  opposition.  The  last  I  heard  of  it  was  in  lectures  at  Plymouth, 
in  October,  1864.  Since  this  time  a  prospectus  has  been  issued 
of  a  work  entitled  '  The  Earth  not  a  Globe ;'  but  whether  it  has 
been  published  I  do  not  know.  The  contents  are  as  follows : — 

'  The  Earth  a  Plane — How  circumnavigated. — How  time  is  lost  or 
gained. — Why  a  ship's  hull  disappears  (when  outward  bound)  before 
the  mast-head. — Why  the  Polar  Star  sets  when  we  proceed  Southward, 
&c. — "Why  a  pendulum  vibrates  with  less  velocity  at  the  Equator  than 
at  the  Pole. — The  allowance  for  rotundity  supposed  to  be  made  by 

x  2 


308  A  BUDGET   OF  PABADOXES. 

surveyors,  not  made  in  practice. — Measurement  of  Arcs  of  the  Meridian 
unsatisfactory. — Degrees  of  Longitude  North  and  South  of  the  Equator 
considered. — Eclipses  and  Earth's  form  considered. — The  Earth  no 
motion  on  axis  or  in  orbit. — How  the  Sun  moves  above  the  Earth's 
surface  concentric  with  the  North  Pole. — Cause  of  Day  and  Night, 
Winter  and  Summer ;  the  long  alternation  of  light  and  darkness  at  the 
Pole. — Cause  of  the  Sun  rising  and  setting. — Distance  of  the  Sun  from 
London,  4,028  miles — How  measured. — Challenge  to  Mathematicians. 
— Cause  of  Tides. — Moon  self-luminous,  NOT  a  reflector. — Cause  of 
Solar  and  Lunar  eclipses. — Stars  not  worlds ;  their  distance. — Earth,  the 
only  material  world ;  its  true  position  in  the  universe;  its  condition  and 
ultimate  destruction  by  fire  (2  Peter  iii.),  &c.' 

I  wish  there  were  geoplatylogical  lectures  in  every  town  in 
England  (platylogical,  in  composition,  need  not  mean  babbling). 
The  late  Mr.  Henry  Archer  would,  if  alive,  be  very  much  obliged 
to  me  for  recording  his  vehement  denial  of  the  roundness  of  the 
earth :  he  was  excited  if  he  heard  any  one  call  it  a  globe.  I 
cannot  produce  his  proof  from  the  Pyramids,  and  from  some 
caves  in  Arabia.  He  had  other  curious  notions,  of  course :  I 
should  no  more  believe  that  a  flat  earth  was  a  man's  only  paradox, 
than  I  should  that  Dutens,  the  editor  of  Leibnitz,  was  eccentric 
only  in  supplying  a  tooth  which  he  had  lost  by  one  which  he 
found  in  an  Italian  tomb,  and  fully  believed  that  it  had  once 
belonged  to  Scipio  Africanus,  whose  family  vault  was  discovered, 
it  is  supposed,  in  1780.  Mr.  Archer  is  of  note  as  the  suggester 
of  the  perforated  border  of  the  postage-stamps,  and,  I  think,  of 
the  way  of  doing  it ;  for  this  he  got  4,000£.  reward.  He  was  a 
civil  engineer. 

(August  28,  1865.)  The  '  Zetetic  Astronomy'  has  come  into 
my  hands.  When,  in  1851,  I  went  to  see  the  Great  Exhibition, 
I  heard  an  organ  played  by  a  performer  who  seemed  very  desirous 
to  exhibit  one  particular  stop.  '  What  do  you  think  of  that 
stop?'  I  was  asked. — 'That  depends  on  the  name  of  it,' 
said  I. — '  Oh  !  what  can  the  name  have  to  do  with  the  sound  ? 
"  that  which  we  call  a  rose,"  &c.' — '  The  name  has  everything 
to  do  with  it :  if  it  be  a  flute-stop,  I  think  it  very  harsh ;  but 
if  it  be  a  railway-whistle-stop,  I  think  it  very  sweet.'  So  as 
to  this  book :  if  it  be  childish,  it  is  clever ;  if  it  be  mannish, 
it  is  unusually  foolish.  The  flat  earth,  floating  tremulously 
on  the  sea;  the  sun  moving  always  over  the  flat,  giving  day 
when  near  enough,  and  night  when  too  far  off;  the  self-luminous 
moon,  with  a  semi-transparent  invisible  moon,  created  to  give 
her  an  eclipse  now  and  then ;  the  new  law  of  perspective,  by 
which  the  vanishing  of  the  hull  before  the  masts,  usually  thought 


MORE   ZETETIC   ASTRONOMY.  309 

to  prove  the  earth  globular,  really  proves  it  flat ; — all  these  and 
other  things  are  well  fitted  to  form  exercises  for  a  person  who  is 
learning  the  elements  of  astronomy.  The  manner  in  which  the 
sun  dips  into  the  sea,  especially  in  tropical  climates,  upsets  the 
whole.  Mungo  Park,  I  think,  gives  an  African  hypothesis  which 
explains  phenomena  better  than  this.  The  sun  dips  into  the 
western  ocean,  and  the  people  there  cut  him  in  pieces,  fry  him  in 
a  pan,  and  then  join  him  together  again,  take  him  round  the 
underway,  and  set  him  up  in  the  east.  I  hope  this  book  will  be 
read,  and  that  many  will  be  puzzled  by  it :  for  there  are  many 
whose  notions  of  astronomy  deserve  no  better  fate.  There  is  no 
subject  on  which  there  is  so  little  accurate  conception  as  that  of 
the  motions  of  the  heavenly  bodies.  The  author,  though  confi- 
dent in  the  extreme,  neither  impeaches  the  honesty  of  those 
whose  opinions  he  assails,  nor  allots  them  any  future  incon- 
venience :  in  these  points  he  is  worthy  to  live  on  a  globe,  and  to 
revolve  in  twenty-four  hours. 

(October,  1866.)  A  follower  appears,  in  a  work  dedicated  to 
the  preceding  author :  it  is  '  Theoretical  Astronomy  examined 
and  exposed  by  Common  Sense.'  The  author  has  128  well-stuffed 
octavo  pages.  I  hope  he  will  not  be  the  last.  He  prints  the 
newspaper  accounts  of  his  work :  the  Church  Times  says — not 
seeing  how  the  satire  might  be  retorted — '  We  never  began  to 
despair  of  Scripture  until  we  discovered  that  "  Common  Sense  " 
had  taken  up  the  cudgels  in  its  defence.'  This  paper  considers 
our  author  as  the  type  of  a  Protestant.  The  author  himself,  who 
gives  a  summary  of  his  arguments  in  verse,  has  one  couplet  which 
is  worth  quoting  : — 

How  is't  that  sailors,  bound  to  sea,  with  a  '  globe '  would  never  start, 
But  in  its  place  will  always  take  Mercator's  LEVEL  chart ! 

To  which  I  answer : — 

Why,  really  Mr.  Common  Sense,  you've  never  got  so  far 

As  to  think  Mercator's  planisphere  shows  countries  as  they  are  ; 

It  won't  do  to  measure  distances  ;  it  points  out  how  to  steer, 

But  this  distortion  's  not  for  you  ;  another  is,  I  fear. 

The  earth  must  be  a  cylinder,  if  seaman's  charts  be  true, 

Or  else  the  boundaries,  right  and  left,  are  one  as  well  as  two ; 

They  contradict  the  notion  that  we  dwell  upon  a  plain, 

For  straight  away,  without  a  turn,  will  bring  you  home  again. 

There  are  various  plane  projections;  and  each  one  has  its  use : 

I  wish  a  milder  word  would  rhyme — but  really  you're  a  goose  ! 


310  A   BUDGET   OF  PARADOXES. 

The  great  wish  of  persons  who  expose  themselves  as  above,  is 
to  be  argued  with,  and  to  be  treated  as  reputable  and  refutable 
opponents,  4  Common  Sense '  reminds  us  that  no  amount  of 
'  blatant  ridicule '  will  turn  right  into  wrong.  He  is  perfectly 
correct :  but  then  no  amount  of  bad  argument  will  turn  wrong 
into  right.  These  two  things  balance  ;  and  we  are  just  where  we 
were  :  but  you  should  answer  our  arguments,  for  whom,  I  ask  ? 
Would  reason  convince  this  kind  of  reasoner  ?  The  issue  is  a 
short  and  a  clear  one.  If  these  parties  be  what  I  contend  they  are, 
then  ridicule  is  made  for  them  :  if  not,  for  what  or  for  whom? 
If  they  be  right,  they  are  only  passing  through  the  appointed 
trial  of  all  good  things.  Appeal  is  made  to  the  future  :  and  my 
Budget  is  intended  to  show  samples  of  the  long  line  of  heroes 
who  have  fallen  without  victory,  each  of  whom  had  his  day  of 
confidence  and  his  prophecy  of  success.  Let  the  future  decide : 
they  say  roundly  that  the  earth  is  flat ;  I  say  flatly  that  it  is 
round. 

The  paradoxers  all  want  reason,  and  not  ridicule  :  they  are  all 
accessible,  and  would  yield  to  conviction.  Well  then,  let  them 
reason  with  one  another !  They  divide  into  squads,  each  with  a 
subject,  and  as  many  different  opinions  as  persons  in  each  squad. 
If  they  be  really  what  they  say  they  are,  the  true  man  of  each  set 
can  put  down  all  the  rest,  and  can  come  crowned  with  glory  and 
girdled  with  scalps,  to  the  attack  on  the  orthodox  misbelievers. 
But  they  know,  to  a  man,  that  the  rest  are  not  fit  to  be  reasoned 
with :  they  pay  the  regulars  the  compliment  of  believing  that  the 
only  chance  lies  with  them.  They  think  in  their  hearts,  each  one 
for  himself,  that  ridicule  is  of  fit  appliance  to  the  rest. 

Miranda.  A  book  divided  into  three  parts,  entitled  Souls, 
Numbers,  Stars,  on  the  Neo-Christian  Religion.  .  .  Vol.  i. 
London,  1858,  1859,  1860.  8vo. 

The  name  of  the  author  is  Filopanti.  He  announces  himself 
as  the  49th  and  last  Emanuel :  his  immediate  predecessors  were 
Emanuel  Washington,  Emanuel  Newton,  and  Emanuel  Galileo. 
He  is  to  collect  nations  into  one  family.  He  knows  the  trans- 
migrations of  the  whole  human  race.  Thus  Descartes  became 
William  III.  of  England  :  Eoger  Bacon  became  Boccaccio.  But 
Charles  IX.,  in  retribution  for  the  massacre  of  St.  Bartholomew, 
was  hanged  in  London  under  the  name  of  Barthelemy  for  the 
murder  of  Collard  :  and  many  of  the  Protestants  whom  he  killed 
as  King  of  France  were  shouting  at  his  death  before  the  Old 
Bailey. 


THE   SABBATH— THE   GREAT   PYRAMID.  311 


A  Letter  to  the  members  of  the  Anglo- Biblical  Institute,  dated 
Sept.  7,  1858,  and  signed  'Herman  Heinfetter.'  (Broadsheet.) 

This  gentleman  is  well  known  to  the  readers  of  the  Athenceum, 
in  which,  for  nearly  twenty  years,  he  has  inserted,  as  advertise- 
ments, long  arguments  in  favour  of  Christians  keeping  the  Jew- 
ish Sabbath,  beginning  on  Friday  Evening.  The  present  letter 
maintains  that,  by  the  force  of  the  definite  article,  the  days  of 
creation  may  not  be  consecutive,  but  may  have  any  time — millions 
of  years — between  them.  This  ingenious  way  of  reconciling  the 
author  of  Genesis  and  the  indications  of  geology  is  worthy  to  be 
added  to  the  list,  already  pretty  numerous.  Mr.  Heinfetter  has 
taken  such  pains  to  make  himself  a  public  agitator,  that  I  do  not 
feel  it  to  be  any  invasion  of  private  life  if  I  state  that  I  have 
heard  he  is  a  large  corn-dealer.  No  doubt  he  is  a  member  of  the 
congregation  whose  almanac  has  already  been  described. 

The  great  Pyramid.  Why  was  it  built  ?  And  who  built  it  ?  By 
John  Taylor,  1859,  12mo. 

This  work  is  very  learned,  and  may  be  referred  to  for  the 
history  of  previous  speculations.  It  professes  to  connect  the 
dimensions  of  the  Pyramid  with  a  system  of  metrology  which  is 
supposed  to  have  left  strong  traces  in  the  systems  of  modern 
times ;  showing  the  Egyptians  to  have  had  good  approximate 
knowledge  of  the  dimensions  of  the  earth,  and  of  the  quadrature 
of  the  circle.  These  are  points  on  which  coincidence  is  hard 
to  distinguish  from  intention.  Sir  John  Herschel  noticed  this 
work,  and  gave  several  coincidences,  in  the  Athenceum,  Nos.  1696 
and  1697,  April  28  and  May  5,  1860  :  and  there  are  some  remarks 
by  Mr.  Taylor  in  No.  1701,  June  2,  1860. 

Mr.  Taylor's  most  recent  publication  is — 

The  battle  of  the  Standards  :  the  ancient,  of  four  thousand  years, 
against  the  modern,  of  the  last  fifty  years — the  less  perfect  of 
the  two.  London,  1864,  12mo. 

This  is  intended  as  an  appendix  to  the  work  on  the  Pyramid. 
Mr.  Taylor  distinctly  attributes  the  original  system  to  revelation, 
of  which  he  says  the  Great  Pyramid  is  the  record.  We  are 
advancing,  he  remarks,  towards  the  end  of  the  Christian  Dispensa- 
tion, and  he  adds  that  it  is  satisfactory  to  see  that  we  retain  the 
standards  which  were  given  by  unwritten  revelation  700  years 
before  Moses.  This  is  lighting  the  candle  at  both  ends  ;  for 


B12  A  BUDGET  -OF  PARADOXES. 

myself,  I  shall  not  undertake  to  deny  or  affirm  either  what  is 
said  about  the  dark  past  or  what  is  hinted  about  the  dark  future. 
My  old  friend  Mr.  Taylor  is  well  known  as  the  author  of  the 
argument  which  has  convinced  many,  even  most,  that  Sir  Philip 
Francis  was  Junius  :  pamphlet,  1813  ;  supplement,  1817  ;  second 
edition  l  The  Identity  of  Junius  with  a  distinguished  living  cha- 
racter established,'  London,  1818,  8vo.  He  told  me  that  Sir 
Philip  Francis,  in  a  short  conversation  with  him,  made  only  this 
remark,  '  You  may  depend  upon  it  you  are  quite  mistaken  :'  the 
phrase  appears  to  me  remarkable ;  it  has  an  air  of  criticism  on 
the  book,  free  from  all  personal  denial.  He  also  mentioned  that 
a  hearer  told  him  that  Sir  Philip  said,  speaking  of  writers  on  the 
question, — '  Those  fellows,  for  half-a-crown,  would  prove  that 
Jesus  Christ  was  Junius.' 

Mr.  Taylor  implies,  I  think,  that  he  is  the  first  who  started  the 
suggestion  that  Sir  Philip  Francis  was  Junius,  which  I  have  no 
means  either  of  confirming  or  refuting.  If  it  be  so  [and  I  now 
know  that  Mr.  Taylor  himself  never  heard  of  any  predecessor], 
the  circumstance  is  very  remarkable :  it  is  seldom  indeed  that 
the  first  proposer  of  any  solution  of  a  great  and  vexed  question 
is  the  person  who  so  nearly  establishes  his  point  in  general 
opinion  as  Mr.  Taylor  has  done. 

As  to  the  Junius  question  in  general,  there  is  a  little  bit  of  the 
philosophy  of  horse-racing  which  may  be  usefully  applied.  A 
man  who  is  so  confident  of  his  horse  that  he  places  him  far  above 
any  other,  may  nevertheless,  and  does,  refuse  to  give  odds  against 
all  the  field :  for  many  small  adverse  chances  united  make  a  big 
chance  for  one  or  other  of  the  opponents.  I  suspect  Mr.  Taylor 
has  made  it  at  least  20  to  1  for  Francis  against  any  one  competi- 
tor who  has  been  named  :  but  what  the  odds  may  be  against  the 
whole  field  is  more  difficult  to  settle.  What  if  the  real  Junius 
should  be  some  person  not  yet  named  ? 

Mr.  Jopling,  Leisure  Hour,  May  23,  1863,  relies  on  the 
porphyry  coffer  of  the  Great  Pyramid,  in  which  he  finds  '  the  most 
ancient  and  accurate  standard  of  measure  in  existence.' 

I  am  shocked  at  being  obliged  to  place  a  thoughtful  and 
learned  writer,  and  an  old  friend,  before  such  a  successor  as  he 
here  meets  with.  But  chronological  arrangement  defies  all  other 
arrangement. 

(I  had  hoped  that  the  preceding  account  would  have  met  Mr. 
Taylor's  eye  in  print :  but  he  died  during  the  last  summer.  For 
a  man  of  a  very  thoughtful  and  quiet  temperament,  he  had  a 
curious  turn  for  vexed  questions.  But  he  reflected  very  long  and 


MRS.   ELIZABETH   COTTLE.  313 

very  patiently  before  he  published :  and  all  his  works  are 
valuable  for  their  accurate  learning,  whichever  side  the  reader 
may  take.) 

1859.  The  Cottle  Church. — For  more  than  twenty  years  printed 
papers  have  been  sent  about  in  the  name  of  Elizabeth  Cottle.  It 
is  not  so  remarkable  that  such  papers  should  be  concocted  as  that 
they  should  circulate  for  such  a  length  of  time  without  attract- 
ing public  attention.  Eighty  years  ago  Mrs.  Cottle  might  have 
rivalled  Lieut.  Brothers  or  Joanna  Southcott.  Long  hence,  when 
the  now  current  volumes  of  our  journals  are  well-ransacked  works 
of  reference,  those  who  look  into  them  will  be  glad  to  see  this 
feature  of  our  time  :  I  therefore  make  a  few  extracts,  faithfully 
copied  as  to  type.  The  Italic  is  from  the  New  Testament ;  the 
Koman  is  the  requisite  interpretation  : — 

'  Robert  Cottle  "  was  numbered  (5196)  tvith  the  transgressors  "  at  the 
back  of  the  Church  in  Norwood  Cemetery,  May  12,  1858 — Isa.  liii.  12. 
The  Rev.  J.  G.  Collinson,  Minister  of  St.  James's  Church,  Clapham, 
the  then  district  church,  before  All  Saints  was  built,  read  the  funeral 
service  over  the  Sepulchre  wherein  never  before  man  was  laid. 

1  Hewn  on  the  stone,  "  at  the  mouth  of  the  Sepulchre,"  is  his  name, — 
Robert  Cottle,  born  at,  Bristol,  June  2,  1774;  died  at  Kirkstall  Lodge, 
Clapham  Park,  May  6,  1858.  And  that  day  (May  12,  1858)  was  the 
preparation  (day  and  year  for  "  the  PREPARED  place  for  you  " — Cottleites 
— by  the  widowed  mother  of  the  Father's  house,  at  Kirkstall  Lodge — 
John  xiv.  2,  3.  And  the  Sabbath  (Christmas  Day,  Dec.  25, 1859)  drew 
on  (for  the  resurrection  of  the  Christian  body  on  "the  third  [Protestant 
Snn]-day  " — 1  Cor.  xv.  35).  Why  seek  ye  the  living  (God  of  the  New 
Jerusalem — Heb.  xii.  22  ;  Rev.  iii.  12)  among  the  dead  (men)  :  he  (the 
God  of  Jesus)  is  not  here  (in  the  grave),  but  is  risen  (in  the  person  of 
the  Holy  Ghost,  from  the  supper  of  "  the  dead  in  the  second  death  "  of 
Paganism).  Remember  how  he  spake  unto  you  (in  the  church  of  the 
Rev.  George  Clayton,  April  14,  1839).  I  will  not  drink  henceforth  (at 
this  last  Cottle  supper)  of  the  fruit  of  this  (Trinity)  vine,  until  that  day 
(Christmas  Day,  1859),  when  /(Elizabeth  Cottle)  drink  it  new  with  you 
(Cottleites)  in  my  Father's  Kingdom — John  xv.  If  this  (Trinitarian) 
cup  may  not  pass  away  from  me  (Elizabeth  Cottle,  April  14,  1839), 
except  I  drink  it  ("new  with  you  Cottleites,  in  my  Father's  Kingdom"), 
thy  will  be  done— Matt.  xxvi.  29,  42,  64.  "  Our  Father  which  art  (God) 
in  Heaven,"  hallowed  be  thy  name,  thy  (Cottle)  kingdom  come,  thy  will 
be  done  in  earth,  as  it  is  (done)  in  (the  new)  Heaven  (and  new  earth  of 
the  new  name  of  Cottle — Rev.  xxi.  1 ;  iii.  12). 

'  .  .  .  Queen  Elizabeth,  from  A.D.  1558  to  1566.  And  this  WORD  yet 
once  more  (by  a  second  Elizabeth — the  WORD  of  his  oath)  signifteth  (at 
John  Scott's  baptism  of  the  Holy  Ghost)  the  removing  of  those  thi/tyx 
(those  Gods  and  those  doctrines)  that  are  made  (according  to  the  Creeds 


314  A  BUDGET   OF  PARADOXES. 

and  Commandments  of  men)  that  those  things  (in  the  moral  law  of 
God)  which  cannot  be  shaken  (as  a  rule  of  faith  and  practice)  may 
remain,  wherefore  we  receiving  (from  Elizabeth)  a  kingdom  (of  God,) 
which  cannot  be  moved  (by  Satan)  let  us  have  grace  (in  his  Grace  of 
Canterbury)  whereby  we  may  serve  God  acceptably  (with  the  acceptable 
sacrifice  of  Elizabeth's  body  and  blood  of  the  communion  of  the  Holy 
Ghost)  with  reverence  (for  truth)  and  godly  fear  (of  the  unpardonable  sin 
of  blasphemy  against  the  Holy  Ghost)  for  our  God  (the  Holy  Ghost) 
is  a  consuming  fire  (to  the  nation  that  will  not  serve  him  in  the  Cottle 
Church).  We  cannot  defend  ourselves  against  the  Almighty,  and  if 
He  is  our  defence,  no  nation  can  invade  us. 

'  In  verse  4  the  Church  of  St.  Peter  is  in,  prison  between  four 
quaternions  of  soldiers — the  Holy  Alliance  of  1815.  B/ev.  vii.  i. 
Elizabeth,  the  Angel  of  the  Lord  Jesus  appears  to  the  Jewish  and  Christian 
body  with  the  vision  of  prophecy  to  the  Rev.  Geo.  Clayton  and  his 
clerical  brethren,  April  8th,  1839.  Bhoda  was  the  name  of  her  maid 
at  Putney  Terrace  who  used  to  open  the  door  to  her  Peter,  the  Rev. 
Robert  Ashton,  the  Pastor  of  "the  little  flock"  "of  120  names 
together,  assembled  in  an  upper  (school)  room  "  at  Putney  Chapel,  to 
which  little  flock  she  gave  the  revelation  (Acts  i.  13,  15)  of  Jesus  the 
same  King  of  the  Jews  yesterday  at  the  prayer  meeting,  Dec.  31,  1841, 
and  to-day,  Jan.  1,  1842,  and  for  ever.  See  book  of  Life,  page  24. 
Matt,  xviii.  19,  xxi.  13 — 16.  In  verse  6  the  Italian  body  of  St.  Peter 
is  sleeping  "  in  the  second  death  "  between  the  two  Imperial  soldiers  of 
France  and  Austria.  The  Emperor  of  France  from  Jan.  1,  to  July  11, 
1859,  causes  the  Italian  chains  of  St.  Peter  to  fall  off  from  his  Imperial 
hands. 

'  I  say  unto  thee,  Robert  Ashton,  thou  art  Peter,  a  stone,  and  upon  this 
rock,  of  truth,  will  I  Elizabeth,  the  angel  of  Jesus,  build  my  Cottle 
Church,  and  the  gates  of  hell,  the  doors  of  St.  Peter,  at  Rome,  shall  not 
prevail  against  it — Matt.  xvi.  18.  Rev.  iii.  7 — 12.' 

This  will  be  enough  for  the  purpose.  When  any  one  who 
pleases  can  circulate  new  revelations  of  this  kind,  uninterrupted 
and  unattended  to,  new  revelations  will  cease  to  be  a  good  in- 
vestment of  excentricity.  I  take  it  for  granted  that  the  gentle- 
men whose  names  are  mentioned  have  nothing  to  do  with  the 
circulars  or  their  doctrines.  Any  lady  who  may  happen  to  be 
intrusted  with  a  revelation  may  nominate  her  own  pastor,  or  any 
other  clergyman,  one  of  her  apostles ;  and  it  is  difficult  to  say 
to  what  court  the  nominees  can  appeal  to  get  the  commission 
abrogated. 

March  16,  1865.  During  the  last  two  years  the  circulars  have 
continued.  It  is  hinted  that  funds  are  low  :  and  two  gentlemen 
who  are  represented  as  gone  '  to  Bethlehem  asylum  in  despair ' 
say  that  Mrs.  Cottle  « will  spend  all  that  she  hath,  while  Her 


THE  COTTLE  CHURCH.  315 

Majesty's  Ministers  are  flourishing  on  the  wages  of  sin.'  The 
following  is  perhaps  one  of  the  most  remarkable  passages  in  the 
whole : — 

1  Extol  and  magnify  Him  (Jehovah,  the  Everlasting  God,  see  the 
Magnificat  and  Luke  i.  45,  46 — 68 — 73—79),  that  ridetli  (by  rail  and 
steam  over  land  and  sea,  from  his  holy  habitation  at  Kirkstall  Lodge, 
Psa.  Ixxvii.  19,  20),  upon  the  (Cottle)  heavens,  as  it  were  (Sept.  9, 1864, 
see  pages  21,  170),  upon  an  (exercising,  Psa.  cxxxi.  1),  &orse-(chair, 
bought  of  Mr.  John  Ward,  Leicester-square).'^ 

I  have  pretty  good  evidence  that  there  is  a  clergyman  who 
thinks  Mrs.  Cottle  a  very  sensible  woman. 

[The  Cottle  Church.  Had  I  chanced  to  light  upon  it  at  the 
time  of  writing,  I  should  certainly  have  given  the  following. 
A  printed  letter  to  the  Western  Times,  by  Mr.  Kobert  Cottle, 
was  accompanied  by  a  manuscript  letter  from  Mrs.  Cottle,  appa- 
rently a  circular.  The  date  was  Novr.  1853,  and  the  subject 
was  the  procedure  against  Mr.  Maurice  at  King's  College  for 
doubting  that  Grod  would  punish  human  sins  by  an  existence  of 
torture  lasting  through  years  numbered  by  millions  of  millions  of 
millions  of  millions  (repeat  the  word  millions  without  end,)  &c. 
The  memory  of  Mr.  Cottle  has,  I  think,  a  right  to  the  quotation  : 
he  seems  to  have  been  no  participator  in  the  notions  of  his 
wife : — 

'  The  clergy  of  the  Established  Church,  taken  at  the  round  number 
of  20,000,  may,  in  their  first  estate,  be  likened  to  20,000  gold  blanks, 
destined  to  become  sovereigns,  in  succession, — they  are  placed  between 
the  matrix  of  the  Mint,  when,  by  the  pressure  of  the  screw,  they  receive 
the  impress  that  fits  them  to  become  part  of  the  current  coin  of  the 
realm.  In  a  way  somewhat  analogous  this  great  body  of  the  clergy 
have  each  passed  through  the  crucibles  of  Oxford  and  Cambridge, — 
have  been  assayed  by  the  Bishop's  chaplain,  touching  the  health  of 
their  souls,  and  the  validity  of  their  call  by  the  Divine  Spirit,  and  then 
the  gentle  pressure  of  a  prelate's  hand  upon  their  heads  ;  and  the 
words — "  Receive  the  Holy  Ghost,"  have,  in  a  brief  space  of  time, 
wrought  a  change  in  them,  much  akin  to  the  miracle  of  transnb- 
stantiation — the  priests  are  completed,  and  they  become  the  current 
ecclesiastical  coin  of  our  country.  The  whole  body  of  clergy,  here 
spoken  of,  have  undergone  the  preliminary  induction  of  baptism  and 
confirmation ;  and  all  have  been  duly  ordained,  professing  to  hold  one 
faith,  and  to  believe  in  thie  selfsame  doctrines  !  In  short,  to  be  as 
identical  as  the  20,000  sovereigns,  if  compared  one  with  the  other. 
But  mind  is  not  malleable  and  ductile,  like  gold  ;  and  all  the  prepara- 
tions of  tests,  creeds,  and  catechisms  will  not  insure  uniformity  of 
belief.  No  stamp  of  orthodoxy  will  produce  the  same  impress  on  the 
minds  of  different  men.  Variety  is  manifest,  and  patent,  upon  every- 


316  A  BUDGET   OF  PARADOXES. 

thing  mental  and  material.  The  Almighty  has  not  created,  nor  man 
fashioned,  two  things  alike !  How  futile,  then,  is  the  attempt  to  shape 
and  mould  man's  apprehension  of  divine  truth  by  one  fallible  standard 
of  man's  invention  !  If  proof  of  this  be  required,  an  appeal  might  be 
made  to  history  and  the  experience  of  eighteen  hundred  years.' 

This  is  an  argument  of  force  against  the  reasonableness  of 
expecting  tens  of  thousands  of  educated  readers  of  the  New 
Testament  to  find  the  doctrine  above  described  in  it.  The  lady's 
argument  against  the  doctrine  itself  is  very  striking.  Speaking 
of  an  outcry  on  this  matter  among  the  Dissenters  against  one  of 
their  body,  who  was  the  son  of  '  the  White  Stone  (Rev.  ii.  17),  or 
the  Eoman  cement-maker,'  she  says — 

'  If  the  doctrine  for  which  they  so  wickedly  fight  were  true,  what 
would  become  of  the  black  gentlemen  for  whose  redemption  I  have 
been  sacrificed  from  April  8,  1839.' 

There  are  certainly  very  curious  points  about  this  revelation. 
There  have  been  many  surmises  about  the  final  restoration  of  the 
infernal  spirits,  from  the  earliest  ages  of  Christianity  until  our 
own  day :  a  collection  of  them  would  be  worth  making.  On 
reading  this  in  proof,  I  see  a  possibility  that  by  '  black  gentle- 
men' may  be  meant  the  clergy.  I  suppose  my  first  interpretation 
must  have  been  suggested  by  context :  I  leave  the  point  to  the 
reader's  sagacity. 

The  Problem  of  squaring  the  circle  solved  ;  or,  the  circumference 
and  area  of  the  circle  discovered.  By  James  Smith.  London, 
1859,  8vo. 

On  the  relations  of  a  square  inscribed  in  a  circle.  Bead  at  the 
British  Association,  Sept.  1859,  published  in  the  Liverpool 
Courier,  Oct.  8,  1859,  and  reprinted  in  broadsheet. 

The  question :  Are  there  any  commensurable  relations  between  a 
circle  and  other  Geometrical  figures  ?  Answered  by  a  member 
of  the  British  Association  .  .  .  London,  1860,  8vo. — [This  has 
been  translated  into  French  by  M.  Armand  Grange,  Bordeaux, 
1863,  8vo.] 

The  Quadrature  of  the  Circle.  Correspondence  between  an  emi- 
nent mathematician  and  James  Smith,  Esq.  (Member  of  the 
Mersey  Docks  and  Harbour  Board),  London,  1861,  8vo.  (pp. 
200). 

Letter  to  the  .  .  British  Association  ...  by  James  Smith,  Esq. 
Liverpool,  1861,  8vo. 

Letter  to  the  .  .  British  Association  ...  by  James  Smith,  Esq. 
Liverpool,  1862,  8vo.— [These  letters  the  author  promised  to 
continue.] 


A   GREAT   CYCLOMETER.  317 

A  Nut  to  crack  for  the  readers  of  Professor  De  Morgan's  '  Budget 
of  Paradoxes.'  By  James  Smith,  Esq.  Liverpool,  1863,  8vo. 

Paper  read  at  the  Liverpool  Literary  aad  Philosophical  Society, 
reported  in  the  Liverpool  Daily  Courier,  Jan.  26,  1864.  Re- 
printed as  a  pamphlet. 

The   Quadrature   of  the  circle,  or   the   true   ratio   between   the 
diameter  and  circumference  geometrically  and  mathematically, 
demonstrated.     By  James  Smith,  Esq.     Liverpool,  1865,  8vo. 

[On  the  relations  between  the  dimensions  and  distances  of  the  Sun, 
Moon,  and  Earth  ;  a  paper  read  before  the  Literary  and  Philo- 
sophical Society  of  Liverpool,  Jan.  25,  1864.  By  James  Smith, 
Esq. 

The  British  Association  in  Jeopardy,  and  Dr.  Whewell,  the  Master 
of  Trinity,  in  the  stocks  without  hope  of  escape.  Printed  for 
the  authors  (J.  S.  confessed,  and  also  hidden  under  Nauticus). 
(No  date,  1865). 

The  British  Association  in  Jeopardy,  and  Professor  De  Morgan 
in  the  Pillory  without  hope  of  escape.  London,  1866,  8vo.] 

When  my  work  appeared  in  numbers,  I  had  not  anything  like 
an  adequate  idea  of  Mr.  James  Smith's  superiority  to  the  rest  of 
the  world  in  the  points  in  which  he  is  superior.  He  is  beyond 
a  doubt  the  ablest  head  at  unreasoning,  and  the  greatest  hand  at 
writing  it,  of  all  who  have  tried  in  our  day  to  attach  their  names 
to  an  error.  Common  cyclometers  sink  into  puny  orthodoxy  by 
his  side. 

The  behaviour  of  this  singular  character  induces  me  to  pay  him 
the  compliment  which  Achilles  paid  Hector,  to  drag  him  round 
the  walls  again  and  again.  He  was  treated  with  unusual  notice 
and  in  the  most  gentle  manner.  The  unnamed  mathematician, 
E.  M.  bestowed  a  volume  of  mild  correspondence  upon  him ; 
Rowan  Hamilton  quietly  proved  him  wrong  in  a  way  accessible  to 
an  ordinary  schoolboy ;  Whewell,  as  we  shall  see,  gave  him  the 
means  of  seeing  himself  wrong,  even  more  easily  than  by 
Hamilton's  method.  Nothing  would  do  ;  it  was  small  kick  and 
silly  fling  at  all ;  and  he  exposed  his  conceit  by  alleging  that 
he,  James  Smith,  had  placed  Whewell  in  the  stocks.  He  will 
therefore  be  universally  pronounced  a  proper  object  of  the 
severest  literary  punishment :  but  the  opinion  of  all  who  can  put 
two  propositions  together  will  be  that  of  the  many  strokes  I  have 
given,  the  hardest  and  most  telling  are  my  republications  of  his 
own  attempts  to  reason. 

He  will  come  out  of  my  hands  in  the  position  he  ought  to 
hold,  the  Supreme  Pontiff  of  cyclometers,  the  vicegerent  of  St. 


318  A  BUDGET   OF  PAKADOXES. 

Vitus  upon  earth,  the  Mamamouchi  of  burlesque  on  inference. 
I  begin  with  a  review  of  him  which  appeared  in  the  Athenceum 
of  May  11,  1861.  Mr.  Smith  says  I  wrote  it:  this  I  neither 
affirm  nor  deny ;  to  do  either  would  be  a  sin  against  the  editorial 
system  elsewhere  described.  Many  persons  tell  me  they  know 
me  by  my  style ;  let  them  form  a  guess :  I  can  only  say  that 
many  have  declared  as  above  while  fastening  on  me  something 
which  I  had  never  seen  nor  heard  of. 

The  Quadrature  of  the  Circle :  Correspondence  between  an 
Eminent  Mathematician  and  James  Smith,  Esq.  (Edinburgh, 
Oliver  &  Boyd ;  London,  Simpkin,  Marshall  &  Co.) 

*  A  few  weeks  ago  we  were  in  perpetual  motion.  We  did  not 
then  suppose  that  anything  would  tempt  us  on  a  circle-squaring 
expedition :  but  the  circumstances  of  the  book  above  named  have 
a  peculiarity  which  induces  us  to  give  it  a  few  words. 

Mr.  James  Smith,  a  gentleman  residing  near  Liverpool,  was 
some  years  ago  seized  with  the  morbus  cyclometricus.  The 
symptoms  soon  took  a  denned  form  :  his  circumference  shrank 
into  exactly  3§-  times  his  diameter,  instead  of  close  to  S^j,  which 
the  mathematican  knows  to  be  so  near  to  truth  that  the  error  is 
hardly  at  the  rate  of  a  foot  in  2,000  miles.  This  shrinking  of 
the  circumference  remained  until  it  became  absolutely  necessary 
that  it  should  be  examined  by  the  British  Association.  This  body, 
which  as  Mr.  James  Smith  found  to  his  sorrow,  has  some  interest 
in  'jealously  guarding  the  mysteries  of  their  profession,'  refused 
at  first  to  entertain  the  question.  On  this  Mr.  Smith  changed 
his  'tactics'  and  the  name  of  his  paper,  and  smuggled  in  the 
subject  under  the  form  of  '  The  Kelations  of  a  Circle  inscribed  in 
a  Square' !  The  paper  was  thus  forced  upon  the  Association,  for 
Mr.  Smith  informs  us  that  he  '  gave  the  Section  to  understand 
that  he  was  not  the  man  that  would  permit  even  the  British 
Association  to  trifle  with  him.'  In  other  words,  the  Association 
bore  with  and  were  bored  with  the  paper,  as  the  shortest  way  out 
of  the  matter.  Mr.  Smith  also  circulated  a  pamphlet.  Some 
kind  hearted  man,  who  did  not  know  the  disorder  as  well  as  we 
do,  and  who  appears  in  Mr.  Smith's  handsome  octavo  as  E.  M. 
— the  initials  of  '  eminent  mathematician ' — wrote  to  him  and 
offered  to  show  him  in  a  page  that  he  was  all  wrong.  Mr.  Smith 
thereupon  opened  a  correspondence,  which  is  the  bulk  of  the 
volume.  When  the  correspondence  was  far  advanced,  Mr.  Smith 
announced  his  intention  to  publish.  His  benevolent  instructor — 


ATHENAEUM  BE  VIEW   OF   ME.   SMITH.  319 

we  mean  in  intention — protested  against  the  publication,  saying, 
'  I  do  not  wish  to  be  gibbeted  to  the  world  as  having  been  foolish 
enough  to  enter  upon  what  I  feel  now  to  have  been  a  ridiculous 
enterprise.' 

For  this  Mr.  Smith  cared  nothing  :  he  persisted  in  the  publica- 
tion, and  the  book  is  before  us.  Mr.  Smith  has  had  so  much 
grace  as  to  conceal  his  kind  adviser's  name  under  E.  M.,  that  is 
to  say,  he  has  divided  the  wrong  among  all  who  may  be  suspected 
of  having  attempted  so  hopeless  a  task  as  that  of  putting  a  little 
sense  into  his  head.  He  has  violated  the  decencies  of  private  life. 
Against  the  will  of  the  kind-hearted  man  who  undertook  his 
case,  he  has  published  letters  which  were  intended  for  no  other 
purpose  than  to  clear  his  poor  head  of  a  hopeless  delusion.  He 
deserves  the  severest  castigation  ;  and  he  will  get  it :  his  abuse  of 
confidence  will  stick  by  him  all  his  days.  Not  that  he  has  done 
his  benefactor — in  intention,  again — any  harm.  The  patience 
with  which  E.  M.  put  the  blunders  into  intelligible  form,  and 
the  perseverance  with  which  he  tried  to  find  a  cranny-hole  for 
common  reasoning  to  get  in  at,  are  more  than  respectable  :  they 
are  admirable.  It  is,  we  can  assure  E.  M.,  a  good  thing  that  the 
nature  of  the  circle-squarer  should  be  so  completely  exposed  as  in 
this  volume.  The  benefit  which  he  intended  Mr.  James  Smith 
may  be  conferred  upon  others.  And  we  should  very  much  like 
to  know  his  name,  and  if  agreeable  to  him,  to  publish  it.  As  to 
Mr.  James  Smith,  we  can  only  say  this :  he  is  not  mad.  Madmen 
reason  rightly  upon  wrong  premises :  Mr.  Smith  reasons  wrongly 
upon  no  premises  at  all. 

E.  M.  very  soon  found  out  that,  to  all  appearance,  Mr.  Smith 
got  a  circle  of  3^  times  the  diameter  by  making  it  the  supposition 
to  set  out  with  that  there  was  such  a  circle  ;  and  then  finding 
certain  consequences  which,  so  it  happened,  were  not  inconsistent 
with  the  supposition  on  which  they  were  made.  Error  is  some- 
times self-consistent.  However,  E.  M.,  to  be  quite  sure  of  his 
ground,  wrote  a  short  letter,  stating  what  he  took  to  be  Mr. 
Smith's  hypothesis,  containing  the  following  : — '  On  A  C  as  dia- 
meter, describe  the  circle  D,  which  by  hypothesis  shall  be  equal 
to  three  and  one-eighth  times  the  length  of  AC.  ...  I  beg, 
before  proceeding  further,  to  ask  whether  I  have  rightly  stated 
your  argument.'  To  which  Mr.  Smith  replied : — '  You  have 
stated  my  argument  with  perfect  accuracy.'  Still  E.  M.  went 
on,  and  we  could  not  help,  after  the  above,  taking  these  letters  as 
the  initials  of  Everlasting  Mercy.  At  last,  however,  when  Mr. 
Smith  flatly  denied  that  the  area  of  the  circle  lies  between  those 


320  A  BUDGET   OP  PAKADOXES. 

of  the  inscribed  and  circumscribed  polygons,  E.  M.  was  fairly 
beaten,  and  gave  up  the  task.  Mr.  Smith  was  left  to  write  his 
preface,  to  talk  about  the  certain  victory  of  truth — which,  oddly 
enough,  is  the  consolation  of  all  hopelessly  mistaken  men  ;  to 
compare  himself  with  Galileo ;  and  to  expose  to  the  world  the 
perverse  behaviour  of  the  Astronomer  Royal,  on  whom  he  wanted 
to  fasten  a  conversation,  and  who  replied,  '  It  would  be  a  waste  of 
time,  Sir,  to  listen  to  anything  you  could  have  to  say  on  such  a 
subject.' 

Having  thus  disposed  of  Mr.  James  Smith,  we  proceed  to  a  few 
remarks  on  the  subject :  it  is  one  which  a  journal  would  never 
originate,  but  which  is  rendered  necessary  from  time  to  time  by 
the  attempts  of  the  autopseustic  to  become  heteropseustic.  To 
the  mathematician  we  have  nothing  to  say :  the  question  is,  what 
kind  of  assurance  can  be  given  to  the  world  at  large  that  the 
wicked  mathematicians  are  not  acting  in  concert  to  keep  down 
their  superior,  Mr.  James  Smith,  the  current  Galileo  of  the 
quadrature  of  the  circle. 

Let  us  first  observe  that  this  question  does  not  stand  alone : 
independently  of  the  millions  of  similar  problems  which  exist  in 
higher  mathematics,  the  finding  of  the  diagonal  of  a  square  has 
just  the  same  difficulty,  namely,  the  entrance  of  a  pair  of  lines  of 
which  one  cannot  be  definitely  expressed  by  means  of  the  other. 
We  will  show  the  reader  who  is  up  to  the  multiplication-table 
how  he  may  go  on,  on,  on,  ever  nearer,  never  there,  in  finding  the 
diagonal  of  a  square  from  the  side. 

Write  down  the  following  rows  of  figures,  and  more,  if  you  like, 
in  the  way  described : — 

1     2     5    12     29     70    169    408     985 
1    3    7    17    41    99    239    577    1393 

After  the  second,  each  number  is  made  up  of  double  the  last 
increased  by  the  last  but  one  :  thus,  5  is  1  more  than  twice  2,12 
is  2  more  than  twice  5,  239  is  41  more  than  twice  99.  Now,  take 
out  two  adjacent  numbers  from  the  upper  line,  and  the  one  below 
the  first  from  the  lower  :  as 

70        169 
99. 

Multiply  together  99  and  169,  giving  16,731.  If,  then,  you  will 
say  that  70  diagonals  are  exactly  equal  to  99  sides,  you  are 
in  error  about  the  diagonal,  but  an  error  the  amount  of  which 
is  not  so  great  as  the  16,731st  part  of  the  diagonal.  Similarly, 


ATHENAEUM  REVIEW   CONTINUED.  321 

to  say  that  five  diagonals  make  exactly  seven  sides  does  not  involve 
an  error  of  the  84th  part  of  the  diagonal. 

Now,  why  has  not  the  question  of  crossing  the  square  been  as 
celebrated  as  that  of  squaring  the  circle  ?  Merely  because  Euclid 
demonstrated  the  impossibility  of  the  first'  question,  while  that 
of  the  second  was  not  demonstrated,  completely,  until  the  last 
century. 

The  mathematicians  have  many  methods,  totally  different  from 
each  other,  of  arriving  at  one  and  the  same  result,  their  celebrated 
approximation  to  the  circumference  of  the  circle.  An  intrepid 
calculator  has,  in  our  own  time,  carried  his  approximation  to 
what  they  call  607  decimal  places :  this  has  been  done  by  Mr. 
Shanks,  of  Houghton-le-Spring,  and  Dr.  Rutherford  has  verified 
441  of  these  places.  But  though  607  looks  large,  the  general 
public  will  form  but  a  hazy  notion  of  the  extent  of  accuracy 
acquired.  We  have  seen,  in  Charles  Knight's  English  Cyclo- 
pcedia,  an  account  of  the  matter  which  may  illustrate  the  un- 
imaginable, though  rationally  conceivable,  extent  of  accuracy 
obtained. 

Say  that  the  blood-globule  of  one  of  our  animalcules  is  a 
millionth  of  an  inch  in  diameter.  Fashion  in  thought  a  globe 
like  our  own,  but  so  much  larger  that  our  globe  is  but  a  blood- 
globule  in  one  of  its  animalcules :  never  mind  the  microscope 
which  shows  the  creature  being  rather  a  bulky  instrument.  Call 
this  the  first  globe  above  us.  Let  the  first  globe  above  us  be  but 
a  blood-globule,  as  to  size,  in  the  animalcule  of  a  still  larger 
globe,  which  call  the  second  globe  above  us.  Go  on  in  this  way 
to  the  twentieth  globe  above  us.  Now  go  down  just  as  far  on  the 
other  side.  Let  the  blood-globule  with  which  we  started  be  a 
globe  peopled  with  animals  like  ours,  but  rather  smaller  :  and 
call  this  the  first  globe  below  us.  Take  a  blood-globule  out  of 
this  globe,  people  it,  and  call  it  the  second  globe  below  us  :  and 
so  on  to  the  twentieth  globe  below  us.  This  is  a  fine  stretch  of 
progression  both  ways.  ,Now  give  the  giant  of  the  twentieth 
globe  above  us  the  607  decimal  places,  and,  when  he  has  measured 
the  diameter  of  his  globe  with  accuracy  worthy  of  his  size,  let 
him  calculate  the  circumference  of  his  equator  from  the  607 
places.  Bring  the  little  philosopher  from  the  twentieth  globe 
below  us  with  his  very  best  microscope,  and  set  him  to  see  the 
small  error  which  the  giant  must  make.  He  will  not  succeed, 
unless  his  microscopes  be  much  better  for  his  size  than  ours  are 
for  ours. 

it  must  be  remembered  by  any  one  who  would  laugh  ut 
Y 


322  A  BUDGET   OF  PARADOXES. 

the  closeness  of  the  approximation,  that  the  mathematician 
generally  goes  nearer ;  in  fact  his  theorems  have  usually  no  error 
at  all.  The  very  person  who  is  bewildered  by  the  preceding 
description  may  easily  forget  that  if  there  were  no  error  at  all, 
the  Lilliputian  of  the  millionth  globe  below  us  could  not  find  a 
flaw  in  the  Brobdingnagian  of  the  millionth  globe  above.  The 
three  angles  of  a  triangle,  of  perfect  accuracy  of  form,  are  abso- 
lutely equal  to  two  right  angles ;  no  stretch  of  progression  will 
detect  any  error. 

Now  think  of  Mr.  Lacomme's  mathematical  adviser  (ante,  p.  32) 
making  a  difficulty  of  advising  a  stonemason  about  the  quantity 
of  pavement  in  a  circular  floor  ! 

We  will  now,  for  our  non-calculating  reader,  put  the  matter  in 
another  way.     We  see  that  a  circle-squarer  can  advance,  with  the 
utmost  confidence,  the  assertion  that  when  the  diameter  is  1,000, 
the  circumference  is  accurately  3,125:  the  mathematician  de- 
claring that  it  is  a  trifle  more  than  3,141^.     If  the  squarer  be 
right,  the  mathematician  has  erred  by  about  a  200th  part  of  the 
whole :    or  has  not  kept   his  accounts   right  by  about    10s.  in 
every  100£.     Of  course,  if  he  set  out  with  such  an   error  he  will 
accumulate  blunder  upon  blunder.     Now,  if  there  be  a  process  in 
which  close  knowledge  of  the  circle  is  requisite,  it  is  in  the  predic- 
tion of  the  moon's  place — say,  as  to  time  of  passing  the  meridian 
at  Greenwich — on  a  given  day.     We  cannot  give  the  least  idea  of 
the  complication  of  details  :  but  common  sense  will  tell  us  that 
if  a  mathematician  cannot  find  his  way  round  the  circle  without 
a  relative  error  four  times  as  big  as  a  stockbroker's  commission, 
he  must  needs  be  dreadfully  out  in  his  attempt  to  predict  the 
time  of  passage  of  the  moon.     Now,  what  is  the  fact  ?     His  error 
is  less  than  a  second  of  time,  and  the  moon  takes  27  days  odd  to 
revolve.     That  is  to  say,  setting  out  with  10s.  in  100£.  of  error  in 
his  circumference,  he  gets  within  the  fifth  part  of  a  farthing  in 
100£.  in  predicting  the  moon's  transit.     Now  we   cannot  think 
that  the  respect  in  which  mathematical  science  is  held  is  great 
enough — though  we  find  it  not  small — to  make  this  go  down. 
That  respect  is  founded  upon  a  notion  that  right  ends  are  got  by 
right  means :  it  will  hardly  be  credited  that  the  truth  can  be  got 
to  farthings  out  of  data  which  are  wrong  by  shillings.     Even  the 
celebrated  Hamilton  of  Edinburgh,  who  held  that  in  mathematics 
there  was  no  way  of  going  wrong,  was  fully  impressed  with  the 
belief  that  this  was  because  error  was  avoided  from  the  beginning. 
He  never  went  so  far  as  to  say  that  a  mathematician  who  begins 
wrong  must  end  right  somehow. 


ATHENJEUM  REVIEW   CONTINUED.  323 

There  is  always  a  difficulty  about  the  mode  in  which  the  think- 
ing man  of  common  life  is  to  deal  with  subjects  he  has  not  studied 
to  a   professional  extent.     He  must  form  opinions  on  matters 
theological,  political,  legal,  medical,  and  social.     If  he  can  make 
up  his  mind  to  choose  a  guide,  there  is,  of  course,  no  perplexity  : 
but  on  all  the  subjects  mentioned  the  direction-posts  point  differ- 
ent ways.     Now  why  should  he  not  form  his  opinion  upon  an 
abstract  mathematical  question  ?     Why  not  conclude  that,  as  to 
the  circle,  it  is  possible  Mr.  James  Smith  may  be  the  man,  just 
as  Adam  Smith  was  the  man  of  things  then  to  come,  or  Luther, 
or  Galileo  ?     It  is  true  that  there  is  an  unanimity  among  mathe- 
maticians which  prevails  in  no  other  class :  but  this  makes  the 
chance  of  their  all  being  wrong  only  different  in  degree.     And 
more  than  this,  is  it  not  generally  thought  among  us  that  priests 
and  physicians  were  never  so  much  wrong  as  when  there  was  most 
appearance  of  unanimity  among  them  ?     To  the  preceding  ques- 
tions we  see  no  answer  except  this,  that  the  individual  inquirer 
may  as  rationally   decide  a  mathematical   question  for  himself 
as  a  theological  or  a  medical  question,  so  soon  as  he  can  put 
himself  into  a  position  in  mathematics  level  with  that  in  which 
he  stands  in  theology  or  medicine.     The  every-day  thought  and 
reading  of  common  life  have  a  certain  resemblance  to  the  thought 
and  reading  demanded  by  the  learned  faculties.     The  research, 
the  balance  of  evidence,  the  estimation  of  probabilities,  which  are 
used  in  a  question  of  medicine,  are  closely  akin  in  character,  how- 
ever different  the  matter  of  application,  to  those  which  serve  a 
merchant  to  draw  his  conclusions  about  the  markets.     But  the 
mathematicians  have  methods  of  their  own,  to  which  nothing  in 
common  life  bears  close  analogy,  as  to  the  nature  of  the  results 
or  the  character  of  the  conclusions.     The  logic  of  mathematics  is 
certainly  that  of  common  life  :  but  the  data  are  of  a  different 
species ;  they  do  not  admit  of  doubt.     An  expert  arithmetician, 
such  as  is  Mr.  J.  Smith,  may  fancy  that  calculation,  merely  as 
such,  is  mathematics :  but  the  value  of  his  book,  and  in  this 
point  of  view  it  is  not  small,  is  the  full  manner  in  which  it  shows 
that  a  practised  arithmetician,  venturing  into  the  field  of  mathe- 
matical demonstration,  may  show  himself  utterly  destitute  of  all 
that  distinguishes  the  reasoning  geometrical  investigator  from  the 
calculator. 

And,  further,  it  should  be  remembered  that  in  mathematics 
the  power  of  verifying  results  far  exceeds  that  which  is  found  in 
anything  else:  and  also  the  variety  of  distinct  methods  by  which 


324  A  BUDGET  OF  PARADOXES. 

they  can  be  attained.  It  follows  from  all  this  that  a  person  who 
desires  to  be  as  near  the  truth  as  he  can  will  not  judge  the 
results  of  mathematical  demonstration  to  be  open  to  his  criticism, 
in  the  same  degree  as  results  of  other  kinds.  Should  he  feel 
compelled  to  decide,  there  is  no  harm  done :  his  circle  may  be 
3£  times  its  diameter,  if  it  please  him.  But  we  must  warn  him 
that,  in  order  to  get  this  circle,  he  must,  as  Mr.  James  Smith  has 
done,  make  it  at  home  :  the  laws  of  space  and  thought  beg  leave 
respectfully  to  decline  the  order." 

I  will  insert  now  at  length,  from  the  Athenceum  of  June  8, 
1861,  the  easy  refutation  given  by  my  deceased  friend,  with  the 
remarks  which  precede. 

"  Mr.  James  Smith,  of  whose  performance  in  the  way  of  squaring 
the  circle  we  spoke  some  weeks  ago  in  terms  short  of  entire 
acquiescence,  has  advertised  himself  in  our  columns,  as  our 
readers  will  have  seen.  He  has  also  forwarded  his  letter  to  the 
Liverpool  Albion,  with  an  additional  statement,  which  he  did 
not  make  in  our  journal.  He  denies  that  he  has  violated  the 
decencies  of  private  life,  since  his  correspondent  revised  the 
proofs  of  his  own  letters,  and  his  '  protest  had  respect  only  to 
making  his  name  public.'  This  statement  Mr.  James  Smith 
precedes  by  saying  that  we  have  treated  as  true  what  we  well 
knew  to  be  false ;  and  he  follows  by  saying  that  we  have  not 
read  his  work,  or  we  should  have  known  the  above  facts  to  be 
true.  Mr.  Smith's  pretext  is  as  follows.  His  correspondent 
E.  M.  says,  '  My  letters  were  not  intended  for  publication,  and  I 
protest  against  their  being  published,'  and  he  subjoins  'Therefore 
I  must  desire  that  my  name  may  not  be  used.'  The  obvious 
meaning  is  that  E.  M.  protested  against  the  publication  altogether, 
but,  judging  that  Mr.  Smith  was  determined  to  publish,  desired 
that  his  name  should  not  be  used.  That  he  afterwards  corrected 
the  proofs  merely  means  that  he  thought  it  wiser  to  let  them 
pass  under  his  own  eyes  than  to  leave  them  entirely  to  Mr. 
Smith. 

We  have  received  from  Sir  W.  Kowan  Hamilton  a  proof  that 
the  circumference  is  more  than  3J  diameters,  requiring  nothing 
but  a  knowledge  of  four  books  of  Euclid.  We  give  it  in  brief  as 
an  exercise  for  our  juvenile  readers  to  fill  up.  It  reminds  us  of 
the  old  days  when  real  geometers  used  to  think  it  worth  while 
seriously  to  demolish  pretenders.  Mr.  Smith's  fame  is  now 
assured:  Sir  W.  E.  Hamilton's  brief  and  easy  exposure  will 
procure  him  notice  in  connexion  with  this  celebrated  problem. 


SIR   W.   ROWAN   HAMILTON   ON   TT.  325 

It  is  to  be  shown  that  the  perimeter  of  a  regular  polygon  of  2O 
sides  is  greater  than  3£  diameters  of  the  circle,  and  still  more, 
of  course,  is  the  circumference  of  the  circle  greater  than  3^ 
diameters. 

1.  It  follows  from  the  4th  Book  of  Euclid,  that  the  rectangle 
under  the  side  of  a  regular  decagon  inscribed  in  a  circle,  and  that 
side  increased  by  the  radius,  is  equal  to  the  square  of  the  radius*» 
But  the  product   791(791  +  1280)  is   less  than  1280x1280;  if 
then  the  radius  be  1280  the  side  of  the  decagon  is  greater  than 
791. 

2.  When  a  diameter  bisects  a  chord,  the  square  of  the  chord  is 
equal  to  the  rectangle  under  the  doubles  of  the  segments  of  the 
diameter.     But   the  product    125  (4x1280—125)  is   less  than 
791x791.     If  then  the  bisected  chord  be  a  side  of  the  decagon, 
and  if  the  radius  be  still  1280,  the  double  of  the  lesser  segment 
exceeds  125. 

3.  The  rectangle  under  this  doubled  segment  and  the  radius  is 
equal  to  the  square  of  the  side  of  an  inscribed  regular  polygon  of 
20  sides.     But  the  product   125x1280  is  equal  to  400x400; 
therefore,  the  side  of  the  last-mentioned  polygon  is  greater  than 
400,  if  the  radius  be  still  1280.     In  other  words,  if  the  radius  be 
represented  by  the  new  member  16,  and  therefore  the  diameter 
by  32,  this  side  is  greater  than  5,  and  the  perimeter  exceeds  100. 
So  that,  finally,  if  the  diameter  be    8,   the  perimeter   of  the 
inscribed  regular  polygon  of  20  sides,  and  still  more  the  circum- 
ference of  the  circle,  is  greater  than  25 :  that  is,  the  circumference 
is  more  than  3£  diameters." 

The  last  work  in  the  list  was  thus  noticed  in  the  Athenceum, 
May  27,  1865. 

"  Mr.  James  Smith  appears  to  be  tired  of  waiting  for  his  place 
in  the  Budget  of  Paradoxes,  and  accordingly  publishes  a  long 
letter  to  Prof.  De  Morgan,  with  various  prefaces  and  postscripts. 
The  letter  opens  by  a  hint  that  the  Budget  appears  at  very  long 
intervals,  and  '  apparently  without  any  sufficient  reason  for  it.' 
As  Mr.  Smith  hints  that  he  should  like  to  see  Mr.  De  Morgan, 
whom  he  calls  an  '  elephant  of  mathematics,'  '  pumping  his 
brains '  'behind  the  scenes' — an  odd  thing  for  an  elephant  to  do, 
and  an  odd  place  to  do  it  in — to  get  an  answer,  we  think  he 
may  mean  to  hint  that  the  Budget  is  delayed  until  the  pump  has 
worked  successfully.  Mr.  Smith  is  informed  that  we  have  had 
the  whole  manuscript  of  the  Budget,  excepting  only  a  final 
summing-up,  in  our  hands  since  October,  1863.  [This  does  not 


326  A   BUDGET   OF  PARADOXES. 

refer  to  the  Supplement.]  There  has  been  no  delay :  we  knew 
from  the  beginning  that  a  series  of  historical  articles  would  be 
frequently  interrupted  by  the  things  of  the  day.  Mr.  James 
Smith  lets  out  that  he  has  never  been  able  to  get  a  private  line 
from  Mr.  De  Morgan  in  answer  to  his  communications  :  we  should 
have  guessed  it.  He  says,  '  The  Professor  is  an  old  bird  and  not 
to  be  easily  caught,  and  by  no  efforts  of  mine  have  I  been  able, 
up  to  the  present  moment,  either  to  induce  or  twit  him  into  a 
discussion.  .  .  .  '  Mr.  Smith  curtails  the  proverb :  old  birds 
are  not  to  be  caught  with  chaff,  nor  with  twit,  which  seems  to  be 
Mr.  Smith's  word  for  his  own  chaff,  and,  so  long  as  the  first  letter 
is  sounded,  a  very  proper  word.  Why  does  he  not  try  a  little 
grain  of  sense  ?  Mr.  Smith  evidently  thinks  that,  in  his  character 
as  an  elephant,  the  Professor  has  not  pumped  up  brain  enough  to 
furnish  forth  a  bird.  In  serious  earnest,  Mr.  Smith  needs  no 
answer.  In  one  thing  he  excites  our  curiosity :  what  is  meant  by 
demonstrating  '  geometrically  and  mathematically  ?  " 
I  now  proceed  to  my  original  treatment  of  the  case. 

Mr.  James  Smith  will,  I  have  no  doubt,  be  the  most  uneclipsed 
circle-squarer  of  our  day.  He  will  not  owe  this  distinction  to  his 
being  an  influential  and  respected  member  of  the  commercial 
world  of  Liverpool,  even  though  the  power  of  publishing  which 
his  means  give  him  should  induce  him  to  issue  a  whole  library 
upon  one  paradox.  Neither  will  he  owe  it  to  the  pains  taken 
with  him  by  a  mathematician,  who  corresponded  with  him  until 
the  joint  letters  filled  an  octavo  volume.  Neither  will  he  owe  it 
to  the  notice  taken  of  him  by  Sir  William  Hamilton,  of  Dublin, 
who  refuted  him  in  a  manner  intelligible  to  an  ordinary  student 
of  Euclid,  which  refutation  he  calls  a  remarkable  paradox  easily 
explainable,  but  without  explaining  it.  What  he  will  owe  it  to  I 
proceed  to  show. 

Until  the  publication  of  the  '  Nut  to  Crack '  Mr.  James  Smith 
stood  among  circle-squarers  in  general.  I  might  have  treated 
him  with  ridicule,  as  I  have  done  others :  and  he  says  that  he 
does  not  doubt  he  shall  come  in  for  his  share  at  the  tail  end  of 
my  Budget.  But  I  can  make  a  better  job  of  him  than  so,  as 
Locke  would  have  phrased  it :  he  is  such  a  very  striking  example 
of  something  I  have  said  on  the  use  of  logic  that  I  prefer  to  make 
an  example  of  his  writings.  On  one  point  indeed  he  well  deserves 
the  scutica,  if  not  the  horribile  flagellum.  He  tells  me  that  he 
will  bring  his  solution  to  me  in  such  a  form  as  shall  compel  me 
to  admit  it  as  un  fait  accompli  [une  faute  accomplie  ?]  or  leave 


ARGUMENT   EX   ABSURDO,  327 

myself  open  to  the  humiliating  charge  of  mathematical  ignorance 
and  folly.     He  has  also  honoured  me  with  some  private  letters. 
In  the  first  of  these  he  gives  me  a  '  piece  of  information,'  after 
which  he  cannot  imagine  that  I,  '  as  an  honest  mathematician,' 
can  possibly  have  the  slightest  hesitation  in  admitting  his  solu- 
tion.    There  is  a  tolerable  reservoir  of  modest  assurance  in  a  man 
who  writes  to  a  perfect  stranger  with  what  he  takes  for  an  argu- 
ment, and  gives  an  oblique  threat  of  imputation  of  dishonesty  in 
case  the  argument  be  not  admitted  without  hesitation ;  not  to 
speak  of  the  minor  charges  of  ignorance  and  folly.     All  this  is 
blind  self-confidence,  without  mixture  of  malicious  meaning ;  and 
I  rather  like  it :  it  makes  me  understand  how  Sam  Johnson  came 
to  say  of  his  old  friend  Mrs.  Cobb, — '  I  love  Moll  Cobb  for  her 
impudence.'     I  have  now  done  with  my  friend's  suaviter  in  modo, 
and  proceed  to  his  fortiter  in  re  :  I  shall  show  that  he  has  con- 
victed himself  of  ignorance  and  folly,  with  an  honesty  and  candour 
worthy  of  a  better  value  of  IT. 

Mr.  Smith's  method  of  proving  that  every  circle  is  3^  diameters 
is  to  assume  that  it  is  so, — '  if  you  dislike  the  term  datum,  then, 
by  hypothesis,  let  8  circumferences  of  a  circle  be  exactly  equal  to 
25  diameters,' — and  then  to  show  that  every  other  supposition  is 
thereby  made  absurd.  The  right  to  this  assumption  is  enforced 
in  the  '  Nut '  by  the  following  analogy  : — 

'  I  think  you  (!)  will  not  dare  (!)  to  dispute  my  right  to  this  hypo- 
thesis, when  I  can  prove  by  means  of  it  that  every  other  value  of  IT  will 
lead  to  the  grossest  absurdities  ;  unless  indeed,  you  are  prepared  to 
dispute  the  right  of  Euclid  to  adopt  a  false  line  hypotbetically  for  the 
purpose  of  a  "  reductio  ad  absurdum"  demonstration,  in  pure  geometry.' 

Euclid  assumes  what  he  wants  to  disprove,  and  shows  that  his 
assumption  leads  to  absurdity,  and  so  upsets  itself.  Mr.  Smith 
assumes  what  he  wants  to  prove,  and  shows  that  his  assumption 
makes  other  propositions  lead  to  absurdity.  This  is  enough  for 
all  who  can  reason.  Mr.  James  Smith  cannot  be  argued  with ; 
he  has  the  whip-hand  of  all  the  thinkers  in  the  world.  Montucla 
would  have  said  of  Mr.  Smith  what  he  said  of  the  gentleman  who 
squared  his  circle  by  giving  50  and  49  the  same  square  root,  II  a 
perdu  le  droit  d'etre  frappe  de  U evidence. 

It  is  Mr.  Smith's  habit,  when  he  finds  a  conclusion  agreeing 
with  its  own  assumption,  to  regard  that  agreement  as  proof  of  the 
assumption.  The  following  is  the  '  piece  of  information '  which 
will  settle  me,  if  I  be  honest.  Assuming  TT  to  be  3£,  he  finds  out 


328  A    BUDGET   OI£  PARADOXES. 

by  working  instance  after  instance  that  the  mean  proportional 
between  one-fifth  of  the  area  and  one-fifth  of  eight  is  the  radius. 
That  is, 

.f          25          //Trr2      8  \ 

lf7r  =  -8>  VU  "5)  =  *' 

This  <  remarkable  general  principle '  may  fail  to  establish  Mr. 
Smith's  quadrature,  even  in  an  honest  mind,  if  that  mind  should 
happen  to  know  that,  a  and  b  being  any  two  numbers  whatever, 
we  need  only  assume — 


7T 


a2     ,  //Trr2     b\ 

=          to  get  at  A  /  I  —  .  —      =  r. 
b  *          sV  \  a       aJ 


We  naturally  ask  what  sort  of  glimmer  can  Mr.  Smith  have  of 
the  subject  which  he  professes  to  treat  ?  On  this  point  he  has 
given  satisfactory  information.  I  had  mentioned  the  old  problem 
of  finding  two  mean  proportionals,  as  a  preliminary  to  the  dupli- 
cation of  the  cube.  On  this  mention  Mr.  Smith  writes  as  follows. 
I  put  a  few  words  in  capitals  ;  and  I  write  rq  for  the  sign  of  the 
square  root,  which  embarrasses  small  type  :  — 

'  This  establishes  the  following  infallible  rule,  for  finding  two  mean 
proportionals  OF  EQUAL  VALUE,  and  is  more  than  a  preliminary,  to  the 
famous  old  problem  of  "  Squaring  the  circle."  Let  any  finite  number, 
say  20,  and  its  fourth  part  =  £  (20)  =  5,  be  given  numbers.  Then 
rq  (20  x  5)  =  rq  100  =  10,  is  their  mean  proportional.  Let  this  be 
a  given  mean  proportional  TO  FIND  ANOTHER  MEAN  PROPORTIONAL  OF  EQUAL 

VALUE.      Then  20    x  ^  =20  x    8'*25   =20  x  78125=  15-625  will 
4  4 

be  the  first  number;  as  25  :  16  :  :  rq  20:  rq  8'192:     and  (rq  8'192)2 

X  j  =  8'192  x  '78125  =  6*4    will  be  the  second  number ;  therefore 

4 

rq  (15'625  x  6'4)  =  rq  100  =  10,  is  the  required  mean  proportional 
.  .  .  Now,  my  good  Sir,  however  competent  you  may  be  to  prove 
every  man  a  fool  [not  every  man,  Mr.  Smith  !  only  some ;  pray  learn 
logical  quantification]  who  now  thinks,  or  in  times  gone  by  has  thought, 
the  "  Squaring  of  the  Circle  "  a  possibility ;  I  doubt,  and,  on  the  evi- 
dence afforded  by  your  Budget,  I  cannot  help  doubting,  whether  you 
were  ever  before  competent  to  find  two  mean  proportionals  by  my  unique 
method.' — (Nut,  pp.  47,  48.)  [That  I  never  was,  I  solemnly  declare  !] 

All  readers  can  be  made  to  see  the  following  exposure.  When 
5  and  20  are  given,  a?  is  a  mean  proportional  when  in  5,  re,  20,  5 
is  to  a;  as  x  to  20.  And  x  must  be  10.  But  x  and  y  are  two 
mean  proportionals  when  in  5,  x,  y,  20,  x  is  a  mean  proportional 
between  5  and  y,  and  y  is  a  mean  proportional  between  x  and  20. 
And  these  means  are  a?  =  5  ^  4,  y  =  5  &  16.  But  Mr.  Smith 


EXTRACT   FROM   CAMBRIDGE   TRANSACTIONS.  329 

finds  one  mean,  finds  it  again  in  a  roundabout  way,  and  produces 
10  and  10  as  the  two  (equal !)  means,  in  solution  of  the  *  famous 
old  problem.'  This  is  enough :  if  more  were  wanted,  there  is 
more  where  this  came  from.  Let  it  not  be  forgotten  that  Mr. 
Smith  has  found  a  translator  abroad,  two,  perhaps  three,  followers 
at  home,  and — most  surprising  of  all — a  real  mathematician  to 
try  to  set  him  right.  And  this  mathematician  did  not  discover 
the  character  of  the  subsoil  of  the  land  he  was  trying  to  cultivate 
until  a  goodly  octavo  volume  of  letters  had  passed  and  repassed. 
I  have  noticed,  in  more  quarters  than  one,  an  apparent  want  of 
perception  of  the  full  amount  of  Mr.  Smith's  ignorance  :  persons 
who  have  not  been  in  contact  with  the  non-geometrical  circle- 
squarers  have  a  kind  of  doubt  as  to  whether  anybody  can  carry 
things  so  far.  But  I  am  an  '  old  bird  '  as  Mr.  Smith  himself  calls 
me  ;  a  Simorg,  an  '  all-knowing  Bird  of  Ages '  in  matters  of 
cyclometry. 

The  curious  phenomena  of  thought  here  exhibited  illustrate,  as 
above  said,  a  remark  I  have  long  ago  made  on  the  effect  of  proper 
study  of  logic.  Most  persons  reason  well  enough  on  matter  to 
which  they  are  accustomed,  and  in  terms  with  which  they  are 
familiar.  But  in  unaccustomed  matter,  and  with  use  of  strange 
terms,  few  except  those  who  are  practised  in  the  abstractions  of 
pure  logic  can  be  tolerably  sure  to  keep  their  feet.  And  one  of 
the  reasons  is  easily  stated :  terms  which  are  not  quite  familiar 
partake  of  the  vagueness  of  the  X  and  Y  on  which  the  student  of 
logic  learns  to  see  the  formal  force  of  a  proposition  independently 
of  its  material  elements. 

I  make  the  following  quotation  from  my  fourth  paper  on  logic 
in  the  Cambridge  Transactions : — 

'  The  uncultivated  reason  proceeds  by  a  process  almost  entirely 
material.  Though  the  necessary  law  of  thought  must  determine  the 
conclusion  of  the  ploughboy  as  much  as  that  of  Aristotle  himself,  the 
ploughboy's  conclusion  will  only  be  tolerably  sure  when  the  matter  of 
it  is  such  as  comes  within  his  usual  cognizance.  He  knows  that  geese 
being  all  birds  does  not  make  all  birds  geese,  but  mainly  because  there 
are  ducks,  chickens,  partridges,  &c.  A  beginner  in  geometry,  when 
asked  what  follows  from  "  Every  A  is  B,"  answers  "  Every  B  is  A." 
That  is,  the  necessary  laws  of  thought,  except  in  minds  which  have 
examined  their  tools,  are  not  very  sure  to  work  correct  conclusions 
except  upon  familiar  matter  ...  As  the  cultivation  of  the  individual 
increases,  the  laws  of  thought  which  are  of  most  usual  application  are 
applied  to  familiar  matter  with  tolerable  safety.  But  difficulty  and 
risk  of  error  make  a  new  appearance  with  a  new  subject ;  and  this,  in 
most  cases,  until  new  subjects  are  familiar  things,  unusual  matter 


330  A   BUDGET   OF  PAKADQXES. 

common,  untried  nomenclature  habitual ;  that  is,  until  it  is  a  habit  to 
be  occupied  upon  a  novelty.  It  is  observed  that  many  persons  reason 
well  in  some  things  and  badly  in  others  ;  and  this  is  attributed  to  the 
consequence  of  employing  the  mind  too  much  upon  one  or  another 
subject.  But  those  who  know  the  truth  of  the  preceding  remarks  will 
not  have  far  to  seek  for  what  is  often,  perhaps  most  often,  the  true 
reason  ...  I  maintain  that  logic  tends  to  make  the  power  of  reason 
over  the  unusual  and  unfamiliar  more  nearly  equal  to  the  power  over 
the  usual  and  familiar  than  it  would  otherwise  be.  The  second  is 
increased  ;  but  the  first  is  almost  created.' 

Mr.  James  Smith,  by  bringing  ignorance,  folly,  dishonesty  into 
contact  with  my  name,  in  the  way  of  conditional  insinuation,  has 
done  me  a  good  turn  :  he  has  given  me  right  to  a  freedom  of 
personal  remark  which  I  might  have  declined  to  take  in  the  case 
of  a  person  who  is  useful  and  respected  in  matters  which  he 
understands. 

Tit  for  tat  is  logic  all  the  world  over.  By  the  way,  what  has 
become  of  the  rest  of  the  maxim :  we  never  hear  it  now.  When 
I  was  a  boy,  in  some  parts  of  the  country  at  least,  it  ran  thus  : — 

Tit  for  tat ; 
Butter  for  fat : 
If  you  kill  my  dog, 
I'll  kill  your  cat. 

He  is  a  glaring  instance  of  the  truth  of  the  observations  quoted 
above.  I  will  answer  for  it  that,  at  the  Mersey  Dock  Board,  he 
never  dreams  of  proving  that  the  balance  at  the  banker's  is  larger 
than  that  in  tbe  book  by  assuming  that  the  larger  sum  is  there, 
and  then  proving  that  the  other  supposition — the  smaller  balance 
— is,  upon  that  assumption,  an  absurdity.  He  never  says  to 
another  director,  How  can  you  dare  to  refuse  me  a  right  to  assume 
the  larger  balance,  when  you  yourself,  the  other  day,  said, — 
Suppose,  for  argument's  sake,  we  had  80,000£.  at  the  banker's, 
though  you  knew  the  book  only  showed  30,OOOL?  This  is  the 
way  in  which  he  has  supported  his  geometrical  paradox  by  Euclid's 
example  :  and  this  is  not  the  way  he  reasons  at  the  board ;  I  know 
it  by  the  character  of  him  as  a  man  of  business  which  has  reached 
my  ears  from  several  quarters.  But  in  geometry  and  rational 
arithmetic  he  is  a  smatterer,  though  expert  at  computation ;  at 
the  board  he  is  a  trained  man  of  business.  The  language  of 
geometry  is  so  new  to  him  that  he  does  not  know  what  is  meant 
by  '  two  mean  proportionals  :'  but  all  the  phrases  of  commerce  are 
rooted  in  his  mind.  He  is  most  unerasably  booked  in  the  history 
of  the  squaring  of  the  circle,  as  the  speculator  who  took  a  right 


VALUE   OF   INSTANCES   OF  INACCURACY.  331 

to  assume  a  proposition  for  the  destruction  of  other  propositions, 
on  the  express  ground  that  Euclid  assumes  a  proposition  to  show 
that  it  destroys  itself :  which  is  as  if  the  curate  should  demand 
permission  to  throttle  the  squire  because  St.  Patrick  drove  the 
vermin  to  suicide  to  save  themselves  from  slaughter.  He  is  con- 
spicuous as  the  speculator  who,  more  visibly  than  almost  any 
other  known  to  history,  reasoned  in  a  circle  by  way  of  reasoning' 
on  a  circle.  But  what  I  have  chiefly  to  do  with  is  the  force  of 
instance  which  he  has  lent  to  my  assertion  that  men  who  have 
not  had  real  training  in  pure  logic  are  unsafe  reasoners  in  matter 
which  is  not  familiar.  It  is  hard  to  get  first-rate  examples  of 
this,  because  there  are  few  who  find  the  way  to  the  printer  until 
practice  and  reflection  have  given  security  against  the  grossest 
slips.  I  cannot  but  think  that  his  case  will  lead  many  to  take 
what  I  have  said  into  consideration,  among  those  who  are  compe- 
tent to  think  of  the  great  mental  disciplines.  To  this  end  I 
should  desire  him  to  continue  his  efforts,  to  amplify  and  develope 
his  great  principle,  that  of  proving  a  proposition  by  assuming 
it  and  taking  as  confirmation  every  consequence  that  does  not 
contradict  the  assumption. 

Since  my  Budget  commenced,  Mr.  Smith  has  written  me  notes  : 
the  portion  which  I  have  preserved — I  suppose  several  have  been 
mislaid — makes  a  hundred  and  seven  pages  of  note-paper,  closely 
written.  To  all  this  I  have  not  answered  one  word :  but  I  think 
I  cannot  have  read  fewer  than  forty  pages.  In  the  last  letter  the 
writer  informs  me  that  he  will  not  write  at  greater  length  until 
I  have  given  him  an  answer,  according  to  the  '  rules  of  good 
society.'  Did  I  not  know  that  for  every  inch  I  wrote  back  he 
would  return  an  ell  ?  Surely  in  vain  the  net  is  spread  in  the 
eyes  of  anything  that  hath  a  wing.  There  were  several  good 
excuses  for  not  writing  to  Mr.  J.  Smith :  I  will  mention  five. 
First,  I  distinctly  announced  at  the  beginning  of  this  Budget  that 
I  would  not  communicate  with  squarers  of  the  circle.  Secondly, 
any  answer  I  might  choose  to  give  might  with  perfect  propriety 
be  reserved  for  this  article  ;  had  the  imputation  of  incivility  been 
made  after  the  first  note,  I  should  immediately  have  replied  to 
this  effect :  but  I  presumed  it  was  quite  understood.  Thirdly, 
Mr.  Smith,  by  his  publication  of  E.  M.'s  letters  against  the  wish 
of  the  writer,  had  put  himself  out  of  the  pale  of  correspondence. 
Fourthly,  he  had  also  gone  beyond  the  rules  of  good  society  in 
sending  letter  after  letter  to  a  person  who  had  shown  by  his 
silence  an  intention  to  avoid  correspondence.  Fifthly,  these  same 
rules  of  good  society  are  contrived  to  be  flexible  or  frangible  in 


832  A  BUDGET   OF  PAEADOXES. 

extreme  cases :  otherwise  there  would  be  no  living  under  them ; 
and  good  society  would  be  bad.  Father  Aldrovand  has  laid  down 
the  necessary  distinction — '  I  tell  thee,  thou  foolish  Fleming,  the 
text  speaketh  but  of  promises  made  unto  Christians,  and  there  is 
in  the  rubric  a  special  exemption  of  such  as  are  made  to  Welch- 
men.'  There  is  also  a  rubric  to  the  rules  of  good  society  ;  and 
squarers  of  the  circle  are  among  those  whom  there  is  special 
permission  not  to  answer :  they  are  the  wild  Welchmen  of  geo- 
metry, who  are  always  assailing;  but  never  taking,  the  Grarde 
Douloureuse  of  the  circle.  '  At  this  commentary,'  proceeds  the 
story,  '  the  Fleming  grinned  so  broadly  as  to  show  his  whole  case 
of  broad  strong  white  teeth.'  I  know  not  whether  the  Welchman 
would  have  done  the  like,  but  I  hope  Mr.  James  Smith  will :  and 
I  hope  he  has  as  good  a  case  to  show  as  Wilkin  Flammock.  For 
I  wish  him  long  life  and  long  health,  and  should  be  very  glad  to 
see  so  much  energy  employed  in  a  productive  way.  I  hope  he 
wishes  me  the  same  :  if  not,  I  will  give  him  what  all  his  judicious 
friends  will  think  a  good  reason  for  doing  so.  His  pamphlets  and 
letters  are  all  tied  up  together,  and  will  form  a  curious  lot  when 
death  or  cessation  of  power  to  forage  among  book-shelves  shall 
bring  my  little  library  to  the  hammer.  And  this  time  may  not 
be  far  off:  for  I  was  X  years  old  in  A.D.  X2;  not  4  in  A.D.  16,  nor 
5  in  A.D.  25,  but  still  in  one  case  under  that  law.  And  now  I 
have  made  my  own  age  a  problem  of  quadrature,  and  Mr.  J. 
Smith  may  solve  it.  But  I  protest  against  his  method  of  assum- 
ing a  result,  and  making  itself  prove  itself :  he  might  in  this  way, 
as  sure  as  eggs  is  eggs  (a  corruption  of  X  is  X),  make  me  1,864 
years  old,  which  is  a  great  deal  too  much. 

April  5,  1864. — Mr.  Smith  continues  to  write  me  long  letters, 
to  which  he  hints  that  I  am  to  answer.  In  his  last,  of  31  closely 
written  sides  of  note-paper,  he  informs  me,  with  reference  to  my 
obstinate  silence,  that  though  I  think  myself  and  am  thought  by 
others  to  be  a  mathematical  Groliath,  I  have  resolved  to  play  the 
mathematical  snail,  and  keep  within  my  shell.  A  mathematical 
snail !  This  cannot  be  the  thing  so  called  which  regulates  the 
striking  of  a  clock  ;  for  it  would  mean  that  I  am  to  make  Mr. 
Smith  sound  the  true  time  of  day,  which  I  would  by  no  means 
undertake  upon  a  clock  that  gains  19  seconds  odd  in  every  hour 
by  false  quadrature.  But  he  ventures  to  tell  me  that  pebbles 
from  the  sling  of  simple  truth  and  common  sense  will  ultimately 
crack  my  shell,  and  put  me  hors  de  combat.  The  confusion  of 
images  is  amusing  :  Goliath  turning  himself  into  a  snail  to  avoid 
TT  =  3£,  and  James  Smith,  Esq.,  of  the  Mersey  Dock  Board  :  and 


KEFUTATION  BY  A   CANTAB.  333 

put  hors  de  combat — which  should  have  been  cach& — by  pebbles 
from  a  sling.  If  Groliath  had  crept  into  a  snail-shell,  David 
would  have  cracked  the  Philistine  with  his  foot.  There  is  some- 
thing like  modesty  in  the  implication  that  the  crack-shell  pebble 
has  not  yet  taken  effect ;  it  might  have  been  thought  that  the 
slinger  would  by  this  time  have  been  singing — 

And  thrice  [and  one-eighth]  I  routed  all  my  foes, 
And  thrice  [and  one-eighth]  I  slew  the  slain. 

But  he  promises  to  give  the  public  his  nut-cracker  if  I  do  not, 
before  the  Budget  is  concluded,  '  unravel '  the  paradox,  which 
is  the  mathematico-geometrical  nut  he  has  given  me  to  crack. 
Mr.  Smith  is  a  crack  man :  he  will  crack  his  own  nut ;  he  will 
crack  my  shell ;  in  the  mean  time  he  cracks  himself  up.  Heaven 
send  he  do  not  crack  himself  into  lateral  contiguity  with  himself. 

On  June  27  I  received  a  letter,  in  the  handwriting  of  Mr.  James 
Smith,  signed  Nauticus.  I  have  ascertained  that  one  of  the 
letters  to  the  Athenaeum  signed  Nauticus  is  in  the  same  hand- 
writing. I  make  a  few  extracts  : — 

'  .  .  .  The  important  question  at  issue  has  been  treated  by  a  brace 
of  mathematical  birds  with  too  much  levity.  It  may  be  said,  however, 
that  sarcasm  and  ridicule  sometimes  succeed,  where  reason  fails  .  .  . 
Such  a  course  is  not  well  suited  to  a  discussion  .  .  .  For  this  reason 
I  shall  for  the  future  [this  implies  there  has  been  a  past,  so  that 
Nauticus  is  not  before  me  for  the  first  time]  endeavour  to  confine 
myself  to  dry  reasoning  from  incontrovertible  premisses  ...  It  appears 
to  me  that  so  far  as  his  theory  is  concerned  he  comes  off  unscathed. 
You  might  have  found  "  a  hole  in  Smith's  circle  "  (have  you  seen  a 
pamphlet  bearing  this  title?  [I  never  heard  of  it  until  now]),  but 
after  all  it  is  quite  possible  the  hole  may  have  been  left  by  design,  for 
the  purpose  of  entrapping  the  unwary.' 

[On  the  publication  of  the  above,  the  author  of  the  pamphlet 
obligingly  forwarded  a  copy  to  me  of  '  A  Hole  in  Smith's  Circle — 
by  a  Cantab:  Longman  and  Co.,  1859,'  (pp.  15).  'It  is  pity  to 
lose  any  fun  we  can  get  out  of  the  affair,'  says  my  almamaternal 
brother  :  to  which  I  add  that  in  such  a  case  warning  without  joke 
is  worse  than  none  at  all,  as  giving  a  false  idea  of  the  nature  of 
the  danger.  The  Cantab  takes  some  absurdities  on  which  I  have 
not  dwelt :  but  there  are  enough  to  afford  a  Cantab  from  every 
college  his  own  separate  hunting  ground.] 

Does  this  hint  that  his  mode  of  proof,  namely,  assuming  the 
thing  to  be  proved,  was  a  design  to  entrap  the  unwary  ?  if  so,  it 
bangs  Banagher.  Was  his  confounding  two  mean  proportionals 


334  A  BUDGET   OF  PARADOXES. 

with  one  mean  proportional  found  twice  over  a  trick  of  the  same 
intent  ?  if  so,  it  beats  cockfighting.  That  Nauticns  is  Mr.  Smith 
appears  from  other  internal  evidence.  In  1819,  Mr.  J.  C.  Hob- 
house  was  sent  to  Newgate  for  a  libel  on  the  House  of  Commons 
which  was  only  intended  for  a  libel  on  Lord  Erskine.  The  ex- 
Chancellor  had  taken  Mr.  Hobhouse  to  be  thinking  of  him  in  a 
certain  sentence ;  this  Mr.  Hobhouse  denied,  adding,  '  There  is 
but  one  man  in  the  country  who  is  always  thinking  of  Lord 
Erskine.'  I  say  that -there  is  but  one  man  of  our  day  who  would 
couple  me  and  Mr.  James  Smith  as  a  '  brace  of  mathematical 
birds.' 

Mr.  Smith's  '  theory '  is  unscathed  by  me.  Not  a  doubt  about 
it:  but  how  does  he  himself  come  off?  I  should  never  think  of 
refuting  a  theory  proved  by  assumption  of  itself.  I  left  Mr. 
Smith's  TT  untouched :  or,  if  I  put  in  my  thumb  and  pulled  out  a 
plum,  it  was  to  give  a  notion  of  the  cook,  not  of  the  dish.  The 
'  important  question  at  issue'  was  not  the  circle  :  it  was,  wholly 
and  solely,  whether  the  abbreviation  of  James  might  be  spelt 
Jimm.1  This  is  personal  to  the  verge  of  scurrility :  but  in 
literary  controversy  the  challenger  names  the  weapons,  and 
Mr.  Smith  begins  with  charge  of  ignorance,  folly,  and  dishonesty, 
by  conditional  implication.  So  that  the  question  is,  not  the 
personality  of  a  word,  but  its  applicability  to  the  person  desig- 
nated :  it  is  enough  if,  as  the  Latin  grammar  has  it,  Verbum 
personate  concordat  cum  nominative. 

I  may  plead  precedent  for  taking  a  liberty  with  the  orthography 
of  Jem.  An  instructor  of  youth  was  scandalised  at  the  abrupt 
and  irregular — but  very  effective — opening  of  Wordsworth's  little 
piece : — 

A  simple  child 

That  lightly  draws  its  breath, 

And  feels  its  life  in  every  limb, 

What  should  it  know  of  death  ? 

So  he  mended  the  matter  by  instructing  his  pupils  to  read  the 
first  line  thus  : — 

A  simple  child,  dear  brother . 

The  brother,  we  infer  from  sound,  was  to  be  James,  and  the  blank 
must  therefore  be  filled  up  with  Jimb. 

I  will  notice  one  point  of  the  letter,  to  make  a   little  more 

1  The  above  is  explained  in  the  MS.  by  a  paragraph  referring  to  some  anagrams, 
in  one  of  which,  by  help  of  the  orthography  suggested,  a  designation  for  this  cyclometer 
was  obtained  from  the  letters  of  his  name.  (Eo  ) 


MEASUREMENT   OF  THE.   ANGLE.  335 

distinction  between  the  two  birds.  Nauticus  lays  down — quite 
correctly — that  the  sine  of  an  angle  is  less  than  its  circular 
measure.  He  then  takes  3-1416  for  180°,  and  finds  that  36'  is 
•010472.  But  this  is  exactly  what  he  finds  for  the  sine  of  36"  in 
tables:  he  concludes  that  either  3-1416  or  the  tables  must  be 
wrong.  He  does  not  know  that  sines,  as  well  as  TT,  are  inter- 
minable decimals,  of  which  the  tables,  to  save  printing,  only  take 
in  a  finite  number.  He  is  a  six-figure  man  :  let  us  go  thrice  again 
to  make  up  nine,  and  we  have  as  follows: — 

Circular  measure  of  36'      ....     '010471975  .     .     . 

Sine  of  36' -010471784.     .     . 

Excess  of  measure  over  sine  .     .     .     '000000191  .     .     . 

Mr.  Smith  invites  me  to  say  which  is  wrong,  the  quadrature,  or 
the  tables :  I  leave  him  to  guess.  He  says  his  assertions  '  arise 
naturally  and  necessarily  out  of  the  arguments  of  a  circle-squarer:' 
he  might  just  as  well  lay  down  that  all  the  pigs  went  to  market 
because  it  is  recorded  that  4  This  pig  went  to  market.'  I  must 
say  for  circle-squarers  that  very  few  bring  their  pigs  to  so  poor  a 
market.  I  answer  the  above  argument  because  it  is,  of  all  which 
Mr.  James  Smith  has  produced,  the  only  one  which  rises  to  the 
level  of  a  schoolboy:  to  meet  him  halfway  I  descend  to  that 
level. 

Mr.  Smith  asks  me  to  solve  a  problem  in  the  Athenaeum :  and 
I  will  do  it,  because  the  question  will  illustrate  what  is  below 
schoolboy  level. 

Let  x  represent  the  circular  measure  of  an  angle  of  15°,  and  y  half 
the  sine  of  an  angle  of  30°  =  area  of  the  square  on  the  radius  of  a 
circle  of  diameter  unity  =  '25.  If  x  —  y  =  xy,  firstly,  what  is  the 
arithmetical  value  of  xy  ?  secondly,  what  is  the  angle  of  which  xy  re- 
presents the  circular  measure  ? 

If  x  represent  15°  and  y  be  £,  xy  represents  3°  45',  whether 
x— y  be  xy  or  no.  But,  y  being  £,  x— y  is  not  xy  unless  x  be  £, 
that  is,  unless  I2x  or  TT  be  4,  which  Mr.  Smith  would  not 
admit.  How  could  a  person  who  had  just  received  such  a  lesson 
as  I  had  given  immediately  pray  for  further  exposure,  furnishing 
the  stuff  so  liberally  as  this  ?  Is  it  possible  that  Mr.  Smith, 
because  he  signs  himself  Nauticus,  means  to  deny  his  own  very 
regular,  legible,  and  peculiar  hand  ?  It  is  enough  to  make  the 
other  members  of  the  Liverpool  Dock  Board  cry,  Mersey  on  the 
man  ! 

Mr.  Smith  says  that  for  the  future  he  will  give  up  what  he 
calls  sarcasm,  and  confine  himself,  '  as  far  as  possible,'  to  what  ne 


336  A  BUDGET  OF  PAEADOXES. 

calls  dry  reasoning  from  incontrovertible  premisses.  If  I  have 
fairly  taught  him  that  his  sarcasm  will  not  succeed,  I  hope  he 
will  find  that  his  wit's  end  is  his  logic's  beginning. 

I  now  reply  to  a  question  I  have  been  asked  again  and  again 
since  my  last  Budget  appeared : — Why  do  you  take  so  much 
trouble  to  expose  such  a  reasoner  as  Mr.  Smith  ?     I  answer  as  a 
deceased  friend  of  mine  used  to  answer  on  like  occasions — A'man's 
capacity  is  no  measure  of  his  power  to  do  mischief.     Mr.  Smith 
has  untiring  energy,  which  does  something ;  self-evident  honesty 
of  conviction,  which  does  more ;  and  a  long  purse,  which  does 
most   of  all.     He   has  made  at   least  ten   publications,  full  of 
figures  which  few  readers  can  criticize.     A  great  many  people 
are  staggered  to  this  extent,  that  they  imagine  there  must  be 
the  indefinite  something  in   the  mysterious  all  this.     They  are 
brought  to  the  point  of  suspicion  that  the  mathematicians  ought 
not  to  treat  '  all  this '  with  such  undisguised  contempt,  at  least. 
Now  I  have  no  fear  for  TT  :  but  I  do  think  it  possible  that  general 
opinion  might  in  time  demand  that  the  crowd  of  circle-squarers, 
&c.  should  be  admitted  to  the  honours  of  opposition  ;  and  this 
would  be  a  time-tax  of  five  per  cent.,  one  man  with  another,  upon 
those  who  are  better  employed.     Mr.  James  Smith  may  be  made 
useful,  in  hands  which  understand  how  to  do  it,  towards  prevent- 
ing such   opinion   from  growing.     A   speculator  who   expressly 
assumes  what  he  wants  to  prove,  and  argues  that  all  which  con- 
tradicts it  is  absurd,  because  it  cannot  stand  side  by  side  with  his 
assumption,  is  a  case  which  can  be  exposed  to  all.     And  the  best 
person  to  expose  it  is  one  who  has  lived  in  the  past  as  well  as  the 
present,  who  takes  misthinking  from  points  of  view  which  none 
but  a  student  of  history  can  occupy,  and  who  has  something  of  a 
turn  for  the  business. 

Whether  I  have  any  motive  but  public  good  must  be  referred 
to  those  who  can  decide  whether  a  missionary  chooses  his  pursuit 
solely  to  convert  the  heathen.  I  shall  certainly  be  thought  to 
have  a  little  of  the  spirit  of  Col.  Quagg,  who  delighted  in  strapp- 
ing the  Grace-walking  Brethren.  I  must  quote  this  myself:  if  I 
do  not,  some  one  else  will,  and  then  where  am  I  ?  The  Colonel's 
principle  is  described  as  follows : — 

'  I  licks  ye  because  I  kin,  and  because  I  like,  and  because  ye'se 
critters  that  licks  is  good  for.  Skins  ye  have  on,  and  skins  I'll  have 
off ;  hard  or  soft,  wet  or  dry,  spring  or  fall.  Walk  in  grace  if  ye  like 
till  pumpkins  is  peaches  ;  but  licked  ye  must  be  till  your  toe-nails 

drop  off  and  your  noses  bleed  blue  ink.'     And — licked— they—  were — 
accordingly.' 


THE   MOON   HOAX.  337 

I  am  reminded  of  this  by  the  excessive  confidence  with  which 
Mr.  James  Smith  predicted  that  he  would  treat  me  as  Zephaniah 
Stockdolloger  (Sam  Slick  calls  it  slockdollager)  treated  Goliah 
Q.uagg.  He  has  announced  his  intention  of  bringing  me,  with  a 
contrite  heart,  and  clean  shaved, — 4159265.  .  .  razored  down  to 
25, — to  a  camp-meeting  of  circle-squarers.  But  there  is  this 
difference :  Zephaniah  only  wanted  to  pass  the  Colonel's  smithy 
in  peace  ;  Mr.  James  Smith  sought  a  fight  with  me.  As  soon  as 
this  Budget  began  to  appear,  he  oiled  his  own  strap,  and  at- 
tempted to  treat  me  as  the  terrible  Colonel  would  have  treated 
the  inoffensive  brother. 

He  is  at  liberty  to  try  again. 

The  Moon-hoax  ;  or  the  discovery  that  the  moon  has  a  vast  popu- 
lation of  human  beings.  By  Richard  Adams  Locke.  New 
York,  1859,  8vo. 

This  is  a  reprint  of  the  hoax  already  mentioned.  I  suppose 
R.  A.  Locke  is  the  name  assumed  by  M.  Nicollet.  The  publisher 
informs  us  that  when  the  hoax  first  appeared  day  by  day  in  a 
morning  paper,  the  circulation  increased  fivefold,  and  the  paper 
obtained  a  permanent  footing.  Besides  this,  an  edition  of  60,000 
was  sold  off  in  less  than  one  month. 

This  discovery  was  also  published  under  the  name  of  A.  R. 
Grant.  Sohnke's  '  Bibliotheca  Mathematica '  confounds  this 
Grant  with  Professor  R.  Grant  of  Glasgow,  the  author  of  the 
'History  of  Physical  Astronomy,'  who  is  accordingly  made  to 
guarantee  the  discoveries  in  the  moon.  I  hope  Adams  Locke  will 
not  merge  in  J.  C.  Adams,  the  co-discoverer  of  Neptune.  Sohnke 
gives  the  titles  of  three  French  translations  of  the  Moon  hoax 
at  Paris,  of  one  at  Bordeaux,  and  of  Italian  translations  at  Parma, 
Palermo,  and  Milan. 

A  Correspondent,  who  is  evidently  fully  master  of  details, 
which  he  has  given  at  length,  informs  me  that  the  Moon  hoax 
appeared  first  in  the  New  York  Sun,  of  which  R.  A.  Locke 
was  editor.  It  so  much  resembled  a  story  then  recently 
published  by  Edgar  A.  Poe,  in  a  Southern  paper,  '  Adven- 
tures of  Hans  Pfaal,'  that  some  New  York  journals  pub- 
lished the  two  side  by  side.  Mr.  Locke,  when  he  left  the 
New  York  Sun,  started  another  paper,  and  discovered  the 
manuscript  of  Mungo  Park ;  but  this  did  not  deceive.  The 
Sun,  however,  continued  its  career,  and  had  a  great  success  in 
an  account  of  a  balloon  voyage  from  England  to  America,  in 
seventy-five  hours,  by  Mr.  Monck  Mason,  Mr.  Harrison  Ainsvvorth, 

z 


338  A  BUDGET  OF  PAEADOXES. 

and  others.  I  have  no  doubt  that  M.  Nicollet  was  the  author  of 
the  Moon  hoax,  written  in  a  way  which  marks  the  practised 
Observatory  astronomer  beyond  all  doubt,  and  by  evidence  seen 
in  the  most  minute  details.  Nicollet  had  an  eye  to  Europe.  I 
suspect  that  he  took  Poe's  story,  and  made  it  a  basis  for  his  own. 
Mr.  Locke,  it  would  seem,  when  he  attempted  a  fabrication  for 
himself,  did  not  succeed. 

The  Earth  we  inhabit,  its  past,  present,  and  future.     By  Capt. 
Drayson.     London,  1859,  8vo. 

The  earth  is  growing ;  absolutely  growing  larger  :  its  diameter 
increases  three-quarters  of  an  inch  per  mile  every  year.  The 
foundations  of  our  buildings  will  give  way  in  time :  the  tele- 
graph cables  break,  and  no  cause  ever  assigned  except  ships' 
anchors,  and  such  things.  The  book  is  for  those  whose  common 
sense  is  unwarped,  who  can  judge  evidence  as  well  as  the  ablest 
philosopher.  The  prospect  is  not  a  bad  one,  for  population  in- 
creases so  fast  that  a  larger  earth  will  be  wanted  in  time,  unless 
emigration  to  the  Moon  can  be  managed,  a  proposal  of  which 
it  much  surprises  me  that  Bishop  Wilkins  has  a  monopoly. 

Athenceum,  August  19,  1865.  Notice  to  Correspondents, 
'  R.  "W. — If  you  will  consult  the  opening  chapter  of  the  Budget  of 
Paradoxes,  you  will  see  that  the  author  presents  only  works  in  his 
own  library  at  a  given  date ;  and  this  for  a  purpose  explained.  For 
ourselves  we  have  carefully  avoided  allowing  any  writers  to  present 
themselves  in  our  columns  on  the  ground  that  the  Budget  has  passed 
them  over.  We  gather  that  Mr.  De  Morgan  contemplates  additions  at 
a  future  time,  perhaps  in  a  separate  and  augmented  work  4  if  so,  those 
who  complain  that  others  of  no  greater  claims  than  themselves  have 
been  ridiculed  may  find  themselves  where  they  wish  to  be.  We  have 
done  what  we  can  for  you  by  forwarding  your  letter  to  Mr.  De  Morgan.* 

The  author  of  i  An  Essay  on  the  Constitution  of  the  Earth,* 
published  in  1844,  demanded  of  the  Athenceum,  as  an  act 
of  fairness,  that  a  letter  from  him  should  be  published,  proving 
that  he  had  as  much  right  to  be  '  impaled '  as  Capt.  Drayson, 
He  holds,  on  speculative  grounds,  what  the  other  claims  to 
have  proved  by  measurement,  namely,  that  the  earth  is  growing; 
and  he  believes  that  in  time — a  good  long  time,  not  owr  time— 
the  earth  and  other  planets  may  grow  into  suns,  with  systems  of 
their  own. 

This  gentleman  sent  me  a  copy  of  his  work,  after  the  -com- 
mencement of  my  Budget  ;  but  I  have  no  recollection  of  having 


IMPALEMENT   BY  REQUEST.  339 

received  it,  and  I  cannot  find  it  on  the  (nursery  ?  quarantine  ?) 
shelves  on  which  I  keep  my  unestablished  discoveries.  Had  I 
known  of  this  work  in  time,  (see  the  Introduction)  I  should  of 
course,  have  impaled  it  (heraldically)  with  the  other  work  ;  but 
the  two  are  very  different.  Capt.  Drayson  professes  to  prove  his 
point  by  results  of  observation  ;  and  I  think  he  does  not  succeed. 
The  author  before  me  only  speculates  ;  and  a  speculator  can  get 
any  conclusion  into  his  premises,  if  he  will  only  build  or  hire 
them  of  shape  and  size  to  suit.  It  reminds  me  of  a  statement  I 
heard  years  ago,  that  a  score  of  persons,  or  near  it,  were  to  dine 
inside  the  skull  of  one  of  the  aboriginal  animals,  dear  little 
creatures  1  Whereat  I  wondered  vastly,  nothing  doubting  ;  facts 
being  stubborn  and  not  easy  drove,  as  Mrs.  Gamp  said.  But  I 
soon  learned  that  the  skull  was  not  a  real  one,  but  artificially 
constructed  by  the  methods — methods  which  have  had  striking 
verifications,  too — which  enable  zoologists  to  go  the  whole  hog 
by  help  of  a  toe  or  a  bit  of  tail.  This  took  off  the  edge  of  the 
wonder :  a  hundred  people  can  dine  inside  an  inference,  if  you 
draw  it  large  enough.  The  method  might  happen  to  fail  for 
once  :  for  instance,  the  toe-bone  might  have  been  abnormalised 
by  therian  or  saurian  malady ;  and  the  possibility  of  such  failure, 
even  when  of  small  probability,  is  of  great  alleviation.  The 
author  before  me  is,  apparently,  the  sole  fabricator  of  his  own 
premises.  With  vital  force  in  the  earth  and  continual  creation  on 
the  part  of  the  original  Creator,  he  expands  our  bit  of  a  residence 
as  desired.  But,  as  the  Newtoness  of  Cookery  observed,  First 
catch  your  hare.  When  this  is  done,  when  you  have  a  growing 
earth,  you  shall  dress  it  with  all  manner  of  proximate  causes,  and 
serve  it  up  with  a  growing  Moon  for  sauce,  a  growing  Sun,  if  it 
please  you,  at  the  other  end,  and  growing  planets  for  side-dishes. 
Hoping  this  amount  of  impalement  will  be  satisfactory,  I  go  on  to 
something  else. 

The  Hailesean  System  of  Astronomy.     By  John  Davey  Hailes  (two 
pages  duodecimo,  I860).. 

He  offers  to  take  100,000£.  to  1,000/.  that  he  shows  the  sun  to 
be  less  than  seven  millions  of  miles  from  the  earth.  The  earth 
in  the  centre,  revolving  eastward,  the  sun  revolving  westward, 
so  that  they  '  meet  at  half  the  circle  distance  in  the  24  hours.' 
The  diameter  of  a  circle  being  9839458303,  the  circumference 
is  30911569920. 

The  following  written  challenge  was  forwarded  to  the  Council 
of  the  Astronomical  Society  :  it  will  show  the  '  general  reader ' 

z  2 


340  A  BUDGET  OF  PARADOXES. 

— and  help  him  towards  earning' his  name — what  sort  of  thing's 
come  every  now  and  then  to  our  scientific  bodies.  I  have  added 
punctuation : — 

Challenge. 

1,000  to  30,000. 

Leverrier's   name   stand   placed   first.      Do   the   worthy   Frenchman 

justice. 

By  awarding  him  the  medal  in  a  trice. 
Give  Adams  an  extra — of  which  neck  and  neck  the  race. 
Now  I  challenge  to  meet  them  and  the  F.  R.  S.'s  all, 
For  good  will  and  one  thousand  pounds  to  their  thirty  thousand  withall, 
That  I  produce  a  system,  which  shall  measure  the  time, 
When  the  Sun  was  vertical  to  Gibeon,  afterward  to  Syene. 
To  meet  any  time  in  London — name  your  own  period, 
To  be  decided  by  a  majority  of  twelve  persons — a  President,  odd. 
That  mean,  if  the  twelve  equally  divide,  the  President  decide, 
I  should  prefer  the  Bishop  of  London,  over  the  meeting  to  preside. 

JOHN  DAVY  HAILES. 
Feb.  17,  1847. 

Mr.  Hailes  still  issues  his  flying  sheets.  The  last  I  have  met 
with  (October  7,  1863)  informs  us  that  the  latitude  of  England 
is  slowly  increasing,  which  is  the  true  cause  of  the  alteration  in 
the  variation  of  the  magnet. 

[Mr.  Hailes  continues  his  researches.  Witness  his  new 
Hailesean  system  of  Astronomy,  displaying  Joshua's  miracle- 
time,  origin  of  time  from  science,  with  Bible  and  Egyptian 
history.  Eewards  offered  for  astronomical  problems.  With 
magnetism,  &c.  &c.  Astronomical  challenge  to  all  the  world. 
Published  at  Cambridge,  in  1865.  The  author  agrees  with 
Newton  in  one  marked  point  Errores  quam  minimi  non  sunt 
contemnendi,  says  Isaac :  meaning  in  figures,  not  in  ortho- 
graphy. Mr.  Hailes  enters  into  the  spirit,  both  positive  and 
negative,  of  this  dictum,  by  giving  the  distance  of  Sidius  from 
the  centre  of  the  earth  at  163,162,008  miles  10  feet  8  inches  17- 
28ths  of  an  inch.  Of  course,  he  is  aware  that  the  centre  of  figure 
of  the  earth  is  17*1998  inches  from  the  centre  of  gravity.  Which 
of  the  two  is  he  speaking  of  ?] 

The  Divine  Mystery  of  Life.     London  [1861],  18mo.  (pp.  32). 
The  author  has  added  one  class  to  zoology,  which  is  printed  in 
capitals,  as  derived  from  0oe,  life,  not  from  z6on,  animal.     That 
class  is  of  Incorporealia,  order  I.,  Infinitum,  of  one  genus  with- 
out  plurality,  Deus :  order  II.,  Finita,  angels  good  and   evil. 


JOHANNES   VON   GUMPACH.  341 

The  rest  is  all  about  a  triune  system,  with  a  diagram.  The 
author  is  not  aware  that  fyaov  is  not  animal,  but  living  being. 
Aristotle  has  classed  gods  under  £o>a,  and  has  been  called  to 
account  for  it  by  moderns  who  have  taken  the  word  to  mean 
animal. 

Explication  du  Zodiaque  de  Denderah,  des  Pyramides,  et  de 
Genese.  Par  le  Capitaine  au  longcours  Justin  Boblin.  Caei^ 
1861.  8vo. 

Capt.  Eoblin,  having  discovered  the  sites  of  gold  and  diamond 
mines  by  help  of  the  zodiac  of  Denderah,  offered  half  to  the 
shareholders  of  a  company  which  he  proposed  to  form.  One  of 
our  journals,  by  help  of  the  zodiac  of  Esne,  offered,  at  five  francs 
a  head,  to  tell  the  shareholders  the  exact  amount  of  gold  and 
diamonds  which  each  would  get,  and  to  make  up  the  amount 
predicted  to  those  who  got  less.  There  are  moods  of  the  market 
in  England  in  which  this  company  could  have  been  formed :  so 
we  must  not  laugh  at  our  neighbours. 

A  million's  worth  of  property,  and  five  hundred  lives  annually 
lost  at  sea  by  the  Theory  of  Gravitation.  A  letter  on  the  true 
figure  of  the  earth,  addressed  to  the  Astronomer  Royal,  by 
Johannes  von  Gumpach.  London,  1861,  8vo.  (pp.  54). 

The  true  figure  and  dimensions  of  the  earth,  in  a  letter  addressed 
to  the  Astronomer  Royal.  By  Job.  von  Gumpach.  2nd  ed. 
entirely  recast.  London,  1862,  8vo.  (pp.  266). 

Two  issues  of  a  letter  published  with  two  different  title-pages,  one 
addressed  to  the  Secretary  of  the  Royal  Society,  the  other  to 
the  Secretary  of  the  Royal  Astronomical  Society.  It  would  seem 
that  the  same  letter  is  also  issued  with,  two  other  titles,  ad- 
dressed to  the  British  Association  and  the  Royal  Geographical 
Society.  By  Job.  von  Gumpach.  London,  1862,  8vo. 

Baby- Worlds.  An  essay  on  the  nascent  members  of  our  solar 
household.  By  Job.  von  Gumpach.  London,  1863,  8vo. 

The  earth,  it  appears,  instead  of  being  flattened,  is  elongated 
at  the  poles  :  by  ignorance  of  which  the  loss  above  mentioned 
occurs  yearly.  There  is,  or  is  to  be,  a  substitute  for  attraction 
and  an  'application  hitherto  neglected,  of  a  recognised  law  of 
optics  to  the  astronomical  theory,  showing  the  true  orbits  of  the 
heavenly  bodies  to  be  perfectly  circular,  and  their  orbital  motions 
to  be  perfectly  uniform : '  all  irregularities  being,  I  suppose, 
optical  delusions.  Mr.  Von  Gumpach  is  a  learned  man  ;  what 
else,  time  must  show. 


342  A   BUDGET   OF   PAKADOXES. 


Perpetuum  Mobile  :  or  Search  for  self-motive  Power.     By  Henry 
Dircks.     London,  1861,  8vo. 

A  useful  collection  on  the  history  of  the  attempts  at  perpetual 
motion,  that  is,  at  obtaining  the  consequences  of  power  without 
any  power  to  produce  them.  September  7, 1863,  a  correspondent 
of  the  Times  gave  an  anecdote  of  Greorge  Stephenson,  which  he 
obtained  from  Eobert  Stephenson.  A  perpetual  motionist  wanted 
to  explain  his  method  ;  to  which  Greorge  replied — '  Sir !  I  shall 
believe  it  when  I  see  you  take  yourself  up  by  the  waistband,  and 
carry  yourself  about  the  room.'  Never  was  the  problem  better 
stated. 

There  is  a  paradox  of  which  I  ought  to  give  a  specimen,  I  mean 
the  slander-paradox ;  the  case  of  a  person  who  takes  it  into  his 
head,  upon  evidence  furnished  entirely  by  the  workings  of  his 
own  thoughts,  that  some  other  person  has  committed  a  foul  act 
of  which  the  world  at  large  would  no  more  suppose  him  guilty 
than  they  would  suppose  that  the  earth  is  a  flat  bordered  by  ice. 
If  I  were  to  determine  on  giving  cases  in  which  the  self-deluded^ 
person  imagines  a  conspiracy  against  himself,  there  would  be  no 
end  of  choices.  Many  of  the  grosser  cases  are  found  at  last  to 
be  accompanied  by  mental  disorder,  and  it  is  difficult  to  avoid 
referring  the  whole  class  to  something  different  from  simple  misuse 
of  the  reasoning  power.  The  first  instance  is  one  which  puts  in 
a  strong  light  the  state  of  things  in  which  we  live,  brought  about 
by  our  glorious  freedom  of  thought,  speech,  and  writing.  The 
Government  treated  it  with  neglect,  the  press  with  silent  con- 
tempt, and  I  will  answer  for  it  many  of  my  readers  now  hear  of 
it  for  the  first  time,  when  it  comes  to  be  enrolled  among  circle- 
squarers  and  earth-stoppers,  where,  as  the  old  philosophers  said, 
it  will  not  gravitate,  being  in  proprio  loco. 

1862.  On  new  year's  day,  1862,  when  the  nation  was  in  the 
full  tide  of  sympathy  with  the  Queen,  and  regret  for  its  own  loss, 
a  paper  called  the  Free  Press  published  a  number  devoted  to  the 
consideration  of  the  causes  of  the  death  of  the  Prince  Consort. 
It  is  so  rambling  and  inconsecutive  that  it  takes  more  than  one 
reading  to  understand  it.  It  is  against  the  Times  newspaper. 
First,  the  following  insinuation  : — 

'  To  the  legal  mind,  the  part  of  [the  part  taken  by]  the  Times  will 
present  a  primd  facie  case  of  the  gravest  nature,  in  the  evident  fore- 
knowledge of  the  event,  and  the  preparation  to  turn  it  to  account 
when  it  should  have  occurred.  The  article  printed  on  Saturday  must 


SLANDER  PARADOXES.  343 

have  been  written  on  Friday.     That  article  could  not  have  appeared 
had  the  Prince  been  intended  to  live.' 

Next,  it  is  affirmed  that  the  Times  intended  to  convey  the  idea 
that  the  Prince  had  been  poisoned. 

'Up  to  this  point  we  are  merely  dealing  with  words  which  the 
Times  publishes,  and  these  can  leave  not  a  shadow  of  doubt  that 
there  is  an  intention  to  promulgat3  the  idea  that  Prince  Albert  had 
been  poisoned.' 

The  article  then  goes  on  with  a  strange  olio  of  insinuations  to 
the  effect  that  the  Prince  was  the  obstacle  to  Russian  intrigue, 
and  that  if  he  should  have  been  poisoned, — which  the  writer 
strongly  hints  may  have  been  the  case, —  some  Minister  under  the 
influence  of  Russia  must  have  done  it.  Enough  for  this  record. 
Un  sot  trouve  toujours  un  plus  sot  qui  Vadmire :  who  can  he  be 
in  this  case  ? 

1846.  At  the  end  of  this  year  arose  the  celebrated  controversy 
relative  to  the  discovery  of  Neptune.  Those  who  know  it  are 
well  aware  that  Mr.  Adams's  now  undoubted  right  to  rank  with 
Le  Verrier  was  made  sure  at  the  very  outset  by  the  manner  in  which 
Mr.  Airy,  the  Astronomer  Royal,  came  forward  to  state  what  had 
taken  place  between  himself  and  Mr.  Adams.  Those  who  know 
all  the  story  about  Mr.  Airy  being  arrested  in  his  progress  by  the 
neglect  of  Mr.  Adams  to  answer  a  letter,  with  all  the  imputations 
which  might  have  been  thrown  upon  himself  for  laxity  in  the 
matter,  know  also  that  Mr.  Airy's  conduct  exhibited  moral 
courage,  honest  feeling,  and  willingness  to  sacrifice  himself,  if 
need  were,  to  the  attainment  of  the  ends  of  private  justice,  and 
the  establishment  of  a  national  claim.  A  writer  in  a  magazine, 
in  a  long  and  elaborate  article,  argued  the  supposition — put  in 
every  way  except  downright  assertion,  after  the  fashion  of  such 
things — that  Mr.  Airy  had  communicated  Mr.  Adams's  results  to 
M.  Le  Verrier,  with  intention  that  they  should  be  used.  His  pre- 
sumption as  to  motive  is  that,  had  Mr.  Adams  been  recognised, 
'  then  the  discovery  must  have  been  indisputably  an  Englishman's, 
and  that  Englishman  not  the  Astronomer  Royal.'  Mr.  Adams's 
conclusions  were  '  retouched  in  France,  and  sent  over  the  year 
after.'  The  proof  given  is  that  it  cannot  be  '  imagined '  other-, 
wise. 

'  Can  it  then  be  imagined  that  the  Astronomer  Royal  received  such 
results  from  Mr.  Adams,  supported  as  they  were  by  Professor  Challis's 
valuable  testimony  as  to  their  probable  accuracy,  and  did  not  bring 


344  A   BUDGET   OF   PARADOXES. 

the  French  astronomer  acquainted  with  them,  especially  as  he  was 
aware  that  his  friend  was  engaged  in  matters  bearing  directly  upon 
these  results  ? ' 

The  whole  argument  the  author  styles  '  evidence  which  I  con- 
sider it  difficult  to  refute.'  He  ends  by  calling  upon  certain 
persons,  of  whom  I  am  one,  to  '  see  ample  justice  done.'  This  is 
the  duty  of  eveiy  one,  according  to  his  opportunities.  So  when 
the  reputed  author — the  article  being  anonymous — was,  in  1849, 
proposed  as  a  Fellow  of  the  Astronomical  Society,  I  joined — if  I 
remember  right,  I  originated — an  opposition  to  his  election,  until 
either  the  authorship  should  be  denied,  or  a  proper  retraction 
made.  The  friends  of  the  author  neither  denied  the  first,  nor 
produced  the  second :  and  they  judged  it  prudent  to  withdraw 
the  proposal.  Had  I  heard  of  any  subsequent  repentance,  I  would 
have  taken  some  other  instance,  instead  of  this  :  should  I  yet 
hear  of  such  a  thing,  I  will  take  care  to  notice  it  in  the  continua- 
tion of  this  list,  which  I  confidently  expect,  life  and  health  per- 
mitting, to  be  able  to  make  in  a  few  years.  This  much  may  be 
said,  that  the  author,  in  a  lecture  on  the  subject,  given  in  1849, 
and  published  with  his  name,  did  not  repeat  the  charge. 

[The  libel  was  published  in  the  '  Mechanics'  Magazine,'  (vol.  for 
1846,  pp.  604-615):  and  the  editor  supported  it  as  follows,  (vol. 
for  1847,  p.  476).  In  answer  to  Mr.  Sheepshanks's  charitable 
hope  that  he  had  been  hoaxed,  he  says  '  Mr.  Sheepshanks  cannot 
certainly  have  read  the  article  referred  to  ...  Severe  and 
inculpatory  it  is — unjust  some  may  deem  it  (though  we  ourselves 
are  out  of  the  number.)  .  .  A  "  hoax  "  forsooth  !  May  we  be  often 
the  dupes  of  such  hoaxes  ! '  He  then  goes  on  to  describe  the 
article  as  directed  against  the  Astronomer  Royal's  alleged  neglect 
to  give  Mr.  Adams  that  '  encouragement  and  protection  '  which 
was  his  due,  and  does  not  hint  one  word  about  the  article  contain- 
ing the  charge  of  having  secretly  and  fraudulently  transmitted 
news  of  Mr.  Adams's  researches  to  France,  that  an  Englishman 
might  not  have  the  honour  of  the  discovery.  Mr.  Sheepshanks 
having  called  this  a  '  deliberate  calumny,'  without  a  particle  of 
proof  or  probability  to  support  it,  the  editor  says  '  what  the 
reverend  gentleman  means  by  this,  we  are  at  a  loss  to  understand.' 
He  then  proceeds  not  to  remember.  I  repeat  here,  what  I  have 
-  said  elsewhere,  that  the  management  of  the  journal  has  changed 
hands  ;  but  from  1846  to  1856,  it  had  the  collar  of  S.S.  (scientific 
slander).  The  prayer  for  more  such  things  was  answered  (See 
pp.  349).] 

I  have  said  that  those  who  are  possessed  with  the  idea  of  con- 


JAMES  IVORY.  345 

Bpiracy  against  themselves  are  apt  to  imagine  both  conspirators  and 
their  bad  motives  and  actions.  A  person  who  should  take  up  the 
idea  of  combination  against  himself  without  feeling  ill-will  and 
originating  accusations  would  be  indeed  a  paradox.  But  such 
a  paradox  has  existed.  It  is  very  well  known,  both  in  and 
beyond  the  scientific  world,  that  the  late  James  Ivory  was  subject 
to  the  impression  of  which  I  am  speaking  ;  and  the  diaries  and 
other  sources  of  anecdote  of  our  day  will  certainly,  sooner  or  later, 
make  it  a  part  of  his  biography.  The  consequence  will  be  that  to 
his  memory  will  be  attached  the  unfavourable  impression  which 
the  usual  conduct  of  such  persons  creates  ;  unless  it  should  happen 
that  some  one  who  knows  the  real  state  of  the  case  puts  the  two 
sides  of  it  properly  together.  Ivory  was  of  that  note  in  the 
scientific  world  which  may  be  guessed  from  Laplace's  description 
of  him  as  the  first  geometer  in  Britain  and  one  of  the  first  in 
Europe.  Being  in  possession  of  accurate  knowledge  of  his  pecu- 
liarity in  more  cases  than  one ;  and  in  one  case  under  his  own 
hand :  and  having  been  able  to  make  full  inquiry  about  him, 
especially  from  my  friend  the  late  Thomas  Galloway — who  came 
after  him  at  Sandhurst— one  of  the  few  persons  with  whom  he 
was  intimate  : — I  have  decided,  after  full  deliberation,  to  forestall 
the  future  biographies. 

That  Ivory  was  haunted  by  the  fear  of  which  I  have  spoken,  to 
the  fullest  extent,  came  to  my  own  public  and  official  knowledge, 
as  Secretary  of  the  Astronomical  Society.  It  was  the  duty  of 
Mr.  Epps,  the  Assistant  Secretary,  at  the  time  when  Francis  Baily 
first  announced  his  discovery  of  the  Flamsteed  Papers,  to  report 
to  me  that  Mr.  Ivory  had  called  at  the  Society's  apartments  to 
inquire  into  the  contents  of  those  papers,  and  to  express  his  hope 
that  Mr.  Baily  was  not  attacking  living  persons  under  the  names 
of  Newton  and  Flamsteed.  Mr.  Gralloway,  to  whom  I  com- 
municated this,  immediately  went  to  Mr.  Ivory,  and  succeeded, 
after  some  explanation,  in  setting  him  right.  This  is  but  one  of 
many  instances  in  which  a  man  of  thoroughly  sound  judgment  in 
every  other  respect  seemed  to  be  under  a  complete  chain  of 
delusions  about  the  conduct  of  others  to  himself.  But  the 
paradox  is  this : — I  never  could  learn  that  Ivory,  passing  his 
life  under  the  impression  that  secret  and  unprovoked  enemies 
were  at  work  upon  his  character,  ever  originated  a  charge, 
imputed  a  bad  motive,  or  allowed  himself  an  uncourteous  expres- 
sion. Some  letters  of  his,  now  in  my  possession,  referring  to  a 
private  matter,  are,  except  in  the  main  impression  on  which  they 
proceed,  unobjectionable  in  every  point :  they  might  have  been 


346  A   BUDGET   OF   PARADOXES. 

written  by  a  cautious  friend,  whose  object  was,  if  possible,  to 
prevent  a  difference  from  becoming  a  duel  without  compromising 
his  principal's  rights  or  character.  Knowing  that  in  some 
quarters  the  knowledge  of  Ivory's  peculiarity  is  more  or  less 
connected  with  a  notion  that  the  usual  consequences  followed,  I 
think  the  preceding  statement  due  to  his  memory. 

In  such  a  record  as  the  present,  which  mixes  up  the  grossest 
speculative  absurdities  with  every  degree  of  what  is  better,  an 
instance  of  another  kind  may  find  an  appropriate  place.  The 
faults  of  journalism,  when  merely  exposed  by  other  journalism 
pass  by  and  are  no  more  regarded.  A  distinct  account  of  an 
undeniable  meanness,  recorded  in  a  work  of  amusement  and  refer- 
ence both,  may  have  its  use  :  such  a  thing  may  act  as  a  warning. 
An  editor  who  is  going  to  indulge  his  private  grudge  may  be 
prevented  from  counting  upon  oblivion  as  a  matter  of  certainty. 

There  are  three  kinds  of  journals,  with  reference  to  the  mode 
of  entrance  of  contributors.  First,  as  a  thing  which  has  been,  but 
which  now  hardly  exists,  there  is  the  journal  in  which  the  editor 
receives  a  fixed  sum  to  find  the  matter.  In  such  a  journal,  every 
article  which  the  editor  can  get  a  friend  to  give  him  is  so  much 
in  his  own  pocket,  which  has  a  great  tendency  to  lower  the  cha- 
racter of  the  articles ;  but  I  am  not  concerned  with  this  point. 
Secondly,  there  is  the  journal  which  is  supported  by  voluntary 
contributions  of  matter,  the  editor  selecting.  Thirdly,  there  is 
the  journal  in  which  the  contributor  is  paid  by  the  proprietors  in 
a  manner  with  which  the  literary  editor  has  nothing  to  do. 

The  third  class  is  the  safe  class,  as  its  editors  know :  and,  as  a 
usual  rule,  they  refuse  unpaid  contributions  of  the  editorial  cast. 
It  is  said  that  when  Canning  declined  a  cheque  forwarded  for  an 
article  in  the  Quarterly,  John  Murray  sent  it  back  with  a  blunt 
threat  that  if  he  did  not  take  his  money  he  could  never  be 
admitted  again.  The  great  publisher  told  him  that  if  men  like 
himself  in  position  worked  for  nothing,  all  the  men  like  himself 
in  talent  who  could  not  afford  it  would  not  work  for  the  Quarterly. 
If  the  above  did  not  happen  between  Canning  and  Murray,  it 
must  have  happened  between  some  other  two.  Now  journals  of 
the  second  class — and  of  the  first,  if  such  there  be — have  a  fault 
to  which  they  alone  are  very  liable,  to  say  nothing  of  the  editorial 
function  (see  the  paper  at  the  beginning,  p.  1 1  et  seq.),  being  very 
much  cramped,  a  sort  of  gratitude  towards  effective  contributors 
leads  the  journal  to  help  their  personal  likes  and  dislikes,  and  to 
sympathise  with  them.  Moreover,  this  sort  of  journal  is  more 
accessible  than  others  to  articles  conveying  personal  imputation  : 


THE   MECHANICS'   MAGAZINE.  347 

and  when  these  provoke  discussion,  the  journal  is  apt  to  take  the 
part  of  the  assailant  to  whom  it  lent  itself  in  the  first  instance. 

Among  the  journals  which  went  all  lengths  with  contributors 
whom  they  valued,  was  the  Mechanics'  Magazine  in  the  period 
1 846-56.  I  cannot  say  that  matters  have  not  mended  in  the  last 
ten  years :  and  I  draw  some  presumption  that  they  have  mended 
from  my  not  having  heard,  since  1856,  of  anything  resembling 
former  proceedings.  And  on  actual  inquiry,  made  since  the  last 
sentence  was  written,  I  find  that  the  property  has  changed  hands, 
the  editor  is  no  longer  the  same,  and  the  management  is  of  a 
different  stamp.  This  journal  is  chiefly  supported  by  voluntary 
articles  :  and  it  is  the  journal  in  which,  as  above  noted,  the  ridicu- 
lous charge  against  the  Astronomer  Eoyal  was  made  in  1849. 
The  following  instance  of  attempt  at  revenge  is  so  amusing  that 
I  select  it  as  the  instance  of  the  defect  which  I  intend  to  illus- 
trate ;  for  its  puerility  brings  out  in  better  relief  the  points 
which  are  not  so  easily  seen  in  more  adult  attempts. 

The  Mechanics'  Magazine^  which  by  its  connexion  with  en- 
gineering, &c.,  had  always  taken  somewhat  of  a  mathematical 
character,  began,  a  little  before  1846,  to  have  more  to  do  with 
abstract  science.  Observing  this,  I  began  to  send  short  communi- 
cations, which  were  always  thankfully  received,  inserted,  and  well 
spoken  of.  Any  one  who  looks  for  my  name  in  that  journal  in 
1846-49,  will  see  nothing  but  the  most  respectful  and  even 
laudatory  mention.  In  May  1849  occurred  the  affair  at  the 
Astronomical  Society,  and  my  share  in  forcing  the  withdrawal  of 
the  name  of  the  alleged  contributor  to  the  journal.  In  February 
1850  occurred  the  opportunity  of  payment.  The  Companion  to 
the  Almanac  had  to  be  noticed,  in  which,  as  then  usual,  was 
an  article  signed  with  my  name.  I  shall  give  the  review  of  this 
article  entire,  as  a  sample  of  a  certain  style,  as  well  as  an  illus- 
tration of  my  point.  The  reader  will  observe  that  my  name  is 
not  mentioned.  This  would  not  have  done ;  the  readers  of  the 
Magazine  would  have  stared  to  see  a  name  of  not  infrequent 
occurrence  in  previous  years  all  of  a  sudden  fallen  from  the 
heaven  of  respect  into  the  pit  of  contempt,  like  Lucifer,  son  of 
the  morning.  But  before  giving  the  review,  I  shall  observe  that 
Mr.  Adams,  in  whose  favour  the  attack  on  the  Astronomer  Koyal 
was  made,  did  not  appreciate  the  favour  ;  and  of  course  did  not 
come  forward  to  shield  his  champion.  This  gave  deadly  offence, 
as  will  appear  from  the  following  passage,  (February  16,  1850)  : — 

"  It  was  our  intention  to  enter  into  a  comparison  of  the  contents  of 
our  Nautical  Almanack  with  those  of  its  rival,  the  Connaismnce  des 


348  A   BUDGET   OF  PARADOXES. 

Temps  ;  but  we  shall  defer  it  for  the  present.  The  Nautical  Almanack 
for  1851  will  contain  Mr.  Adams's  paper  '  On  the  Perturbation  of 
Uranus  ; '  and  when  it  comes,  in  due  course,  before  the  public,  we  are 
quite  sure  that  that  gentleman  will  expect  that  we  shall  again  enter 
upon  the  subject  with  peculiar  delight.  Whilst  we  have  a  thorough 
loathing  for  mean,  cowardly,  crawlers — we  have  an  especial  pleasure 
in  maintaining  the  claims  of  men  who  are  truly  grateful  as  well  as 
highly-talented :  Mr.  Adams,  therefore,  will  find  that  he  cannot  be 
disappointed — and  the  occasion  will  afford  us  an  opportunity  for 
making  the  comparison  to  which  we  have  adverted." 

This  passage  illustrates  what  I  have  said  on  the  editorial  function 
(p.  11).  What  precedes  and  follows  has  some  criticism  on  the 
Government,  the  Astronomer  Eoyal,  &c.,  but  reserved  in  allusion, 
oblique  in  sarcasm,  and  not  fiercely  uncourteous.  The  coarseness 
of  the  passage  I  have  quoted  shews  editorial  insertion,  which  is 
also  shown  by  its  blunder.  The  inserter  is  waiting  for  the 
Almanac  of  1851  that  lie  may  review  Mr.  Adams's  paper,  which  is 
to  be  contained  in  it.  His  own  contributor,  only  two  sentences 
before  the  insertion,  had  said,  c  The  Nautical  Almanac,  we  believe, 
is  published  three  or  four  years  in  advance.'  In  fact,  the 
Almanac  for  1851 — with  Mr.  Adams's  paper  at  the  end — was  pub- 
lished at  the  end  of  1847  or  very  beginning  of  1848;  it  had 
therefore  been  more  than  two  years  before  the  public  when  the 
passage  quoted  was  written.  And  probably  every  person  in  the 
country  who  was  fit  to  review  Mr.  Adams's  paper — and  most  of 
those  who  were  fit  to  read  it — knew  that  it  had  been  widely 
circulated,  in  revise,  at  the  end  of  1846  :  my  copy  has  written 
on  it,  '  2nd  revise,  December  27,  1846,  at  noon,'  in  the  hand- 
writing of  the  Superintendent  of  the  Almanac  ;  and  I  know  that 
there  was  an  extensive  issue  of  these  revises,  brought  out  by  the 
Le-Verrier-and- Adams  discussion.  I  now  give  the  review  of  my- 
self, (February  23,  1850):— 

"THE   BRITISH  ALMANACK  AND   COMPANION. 

"  The  Companion  to  this  Almanack,  for  some  years  after  its  first 
publication,  annually  contained  scientific  articles  by  Sir  J.  Lubbock 
and  others  of  a  high  order  and  great  interest ;  we  have  now,  however, 
closed  the  publication  as  a  scientific  one  in  remembrance  of  what  it 
was,  and  not  in  consequence  of  what  it  is.  Its  list  of  contributors  on 
science,  has  grown  '  small  by  degrees  and  beautifully  less,'  until  it  has 
dwindled  down  to  one — '  a  last  rose  of  summer  left  withering  alone.' 
The  one  contributor  has  contributed  one  paper  '  On  Ancient  and 
Modern  Usage  in  Beckoning.' 

The  learned  critic's  chef  d'osuvre,  is  considered,  by  competent  judges, 


EXTRACT   FROM   MECHANICS'   MAGAZINE.  349 

to  be  an  Essay  on  Old  Almanacks  printed  a  few  years  ago  in  this 
annual,  and  supposed  to  be  written  with,  the  view  of  surpassing  a 
profound  memoir  on  the  same  subject  by  James  0.  Halliwell,  Esq., 
F.R.  and  A.S.S.,  but  the  tremendous  effort  which  the  learned  writer 
then  made  to  excel  many  titled  competitors  for  honours  in  the  antique 
line  appears  to  have  had  a  sad  effect  upon  his  mental  powers — at  any 
rate,  his  efforts  have  since  yearly  become  duller  and  duller ;  happily, 
at  last,  we  should  suppose,  '  the  ancient  and  modern  usage  in  reckon- 
ing '  indicates  the  lowest  point  to  which  the  vis  inertia  of  the  learned 
writer's  peculiar  genius  can  force  him. 

We  will  give  a  few  extracts  from  the  article. 

The  learned  author  says,  '  Those  who  are  accustomed  to  settle  the 
meaning  of  ancient  phrases  by  self-examination  will  find  some  strange 
conclusions  arrived  at  by  us.'  The  writer  never  wrote  a  more  correct 
sentence — it  admits  of  no  kind  of  dispute. 

'  Language  and  counting,'  says  the  learned  author,  '  both  came 
before  the  logical  discussion  of  either.  It  is  not  allowable  to  argue 
that  something  is  or  was,  because  it  ought  to  be  or  ought  to  have 
been.  That  two  negatives  make  an  affirmative,  ought  to  be ;  if  no 
man  have  done  nothing,  the  man  who  has  done  nothing  does  not  exist, 
and  every  man  has  done  something.  Rat  in  Greek,  and  in  uneducated 
English,  it  is  unquestionable  that  '  no  man  has  done  nothing  '  is  only 
an  emphatic  way  of  saying  that  no  man  has  done  anything ;  and  it 
would  be  absurd  to  reason  that  it  could  not  have  been  so,  because  it 
should  not.' — p.  5. 

'But  there  is  another  difference  between  old  and  new  times,  yet 
more  remarkable,  for  we  have  nothing  of  it  now :  whereas  in  things 
indivisible  we  count  with  our  fathers,  and  should  say  in  buying  an 
acre  of  land,  that  the  result  has  no  parts,  and  that  the  purchaser,  till 
he  owns  all  the  ground,  owns  none,  the  change  of  possession  being 
instantaneous.  This  second  difference  lies  in  the  habit  of  considering 
nothing,  nought,  zero,  cipher,  or  whatever  it  may  be  called,  to  be  at  the 
beginning  of  the  scale  of  numbers.  Count  four  days  from  Monday : 
we  should  now  say  Tuesday,  Wednesday,  Thursday,  Friday ;  formerly, 
it  would  have  been  Monday,  Tuesday,  Wednesday,  Thursday.  Had 
we  asked,  what  at  that  rate  is  the  first  day  from  Monday,  all  would 
have  stared  at  a  phrase  they  had  never  heard.  Those  who  were 
capable  of  extending  language  would  have  said,  Why  it  must  be 
Monday  itself :  the  rest  would  have  said,  there  can  be  no  first  day 
from  Monday,  for  the  day  after  is  Tuesday,  which  must  be  the  second 
day  :  Monday,  one  ;  Tuesday,  two.' — p.  10. 

We  assure  our  readers  that  the  whole  article  is  equally  lucid,  and 
its  logic  alike  formal. 

There  are  some  exceedingly  valuable  foot-notes ;  we  give  one  of  the 
most  interesting,  taken  from  the  learned  Mr.  Halliwell's  profound 
book  on  Nursery  Rhymes — a  celebrated  production,  for  which  it  is 
supposed  the  author  was  made  F.R.S. 


350  A  BUDGET  OF  PAKADOXES. 

'  One's  nine, 
Two's  some, 
Three's  a  many, 
Four's  a  penny, 
Five's  a  little  hundred." 

'  The  last  line  refers  to  five  score,  the  so-called  hundred  being  more 
usually  six  score.  The  first  line,  looked  at  etymologically,  is  one  is  not 
one,  and  the  change  of  thought  by  which  nine,  the  decimal  of  one, 
aims  to  be  associated  with  the  decimal  of  plurality  is  curious  : ' — Very. 
This  valuable  and  profound  essay  will  very  probably  be  transferred 
to  the  next  edition  of  the  learned  Mr.  Halliwell's  rare  work,  of  kindred 
worth,  entitled  '  KARA  MATHEMATICA,'  it  will  then  be  deservedly  handed 
down  to  posterity  as  a  covering  for  cheap  trunks — a  most  appropriate 
archive  for  such  a  treasure." 

In  December,  1846,  the  Mechanics'1  Magazine  published  a  libel 
on  Airy  in  the  matter  of  the  discovery  of  Neptune.  In  May, 
1 849,  one  *  *  *  was  to  have  been  brought  forward  for  election  at 
the  Astronomical  Society,  and  was  opposed  by  me  and  others, 
on  the  ground  that  he  was  the  probable  author  of  this  libel, 
and  that  he  would  not,  perhaps  could  not,  deny  it.  [N.B.  I  no 
more  doubt  that  he  was  the  author  than  I  doubt  that  I  am  the 
author  of  this  sentence.]  * 

Accordingly,  *  *  *  was  withdrawn,  and  a  discussion  took 
place,  for  which  see  the  Athenceum,  No.  1126,  May  26,  1849, 
p.  544.  The  Mechanics'1  Magazine  was  very  sore,  but  up  to  this 
day  has  never  ventured  beyond  an  attack  on  Airy,  private  whis- 
perings against  Adams — (see  ante,  p.  348), — and  the  above  against 
myself.  In  due  time,  I  doubt  not  my  name  will  appear  as  one  of 
the  dmes  damnees  of  the  Mechanics"  Magazine.2 

First,  as  to  Mr.  Halliwell.  The  late  Thomas  Stephens  Davies, 
excellent  in  geometry,  and  most  learned  in  its  history,  was 
also  a  good  hand  at  enmity,  though  not  implacable.  He  and  Mr. 
Halliwell,  who  had  long  before  been  very  much  one,  were,  at  this 
date,  very  much  two.  I  do  not  think  T.  S.  Davies  wrote  this 
article ;  and  I  think  that  by  giving  my  reasons  I  shall  do  service 
to  his  memory.  It  must  have  been  written  at  the  beginning  of 
February ;  and  within  three  days  of  that  time  T.  S.  Davies  was 
making  over  to  me,  by  his  own  free  act,  to  be  kept  until  claimed 

1  The  subject  of  this  criticism  is  of  long  past  date,  and  as  it  has  only  been  intro- 
duced by  the  author  as  an  instance  of  faulty  editorship,  I  have  omitted  the  name  of 
the  writer  of  the  libel,  and  a  few  lines  of  further  detail. — ED. 

2  The  editor  of  the  Mechanics'  Magazine  died  soon  after  the  above  was  written. — ED. 


T.   S.  DAVIES  ON  EUCLID.  351 

by  the  relatives,  what  all  who  knew  even  his  writings  knew  that 
he  considered  as  the  most  precious  deposit  he  had  ever  had  in  his 
keeping  —  Homer's  papers.  His  letter  announcing  the  trans- 
mission is  dated  February  2,  1850.  This  is  a  strong  point;  but 
there  is  another  quite  as  strong.  Euclid  and  his  writings  were 
matters  on  which  T.  S.  Da  vies  knew  neither  fear  nor  favour:  he 
could  not  have  written  lightly  about  a  man  who  stood  high  with 
him  as  a  judge  of  Euclid.  Now  in  this  very  letter  of  Feb.  2, 
there  is  a  sentence  which  I  highly  value,  because,  as  aforesaid, 
it  is  on  a  point  on  which  he  would  never  have  yielded  anything, 
to  which  he  had  paid  life-long  attention,  and  on  which  he  had 
the  bias  of  having  long  stood  alone.  In  fact,  knowing — and 
what  I  shall  quote  confirms  me, — that  in  the  matter  of  Euclid 
his  hand  was  against  every  man,  I  expected,  when  I  sent  him  a 
copy  of  my  22-column  article,  '  Eucleides '  in  Smith's  Dictionary, 
to  have  received  back  a  criticism,  that  would  have  blown  me  out 
of  the  water :  and  I  thought  it  not  unlikely  that  a  man  so  well 
up  in  the  subject  might  have  made  me  feel  demolished  on  some 
points.  Instead  of  this,  I  got  the  following :  '  Although  on  one 
or  two  minor  points  I  do  not  quite  accord  with  your  views,  yet 
as  a  whole  and  without  regard  to  any  minor  points,  I  think  you 
»re  the  first  who  has  succeeded  in  a  delineation  of  Euclid  as  a 
geometer,'  All  this  duly  considered,  it  is  utterly  incredible  that 
T*  S.  Da  vies  should  have  written  the  review  in  question.  'And 
yet  Mr.  Halliwell  is  treated  just  as  T.  S.  Davies  would  have 
treated  him,  as  to  tone  and  spirit.  The  inference  in  my  mind  is 
that  we  have  here  a  marked  instance  of  the  joining  of  hatreds 
which  itakes  place  in  journals  supported  by  voluntary  contribu- 
tions of  matter.  Should  anything  ever  have  revived  this  article 
— -and  no  one  ever  knows  what  might  have  been  fished  up  from 
the  forgotten  mass  of  journals — the  treatment  of  Mr.  Halliwell 
would  certainly  have  thrown  a  suspicion  on  T.  S.  Davies,  a  large 
and  regular  contributor  to  the  Magazine..  It  is  good  service  to 
his  memory  to  point  out  what  makes  it  incredible  that  he  should 
have  written  so  unworthy  an  article. 

The  fault  is  this.  There  are  four  extracts  :  the  first  three  are 
perfectly  well  printed.  The  printing  of  the  Mechanics'  Magazine 
was  very  good.  I  was  always  exceedingly  satisfied  with  the 
manner  in  which  ray  articles  appeared,  without  my  seeing  proof. 
Most  likely  these  extracts  were  printed  from  my  printed  paper ; 
if  not  the  extractor  was  a  good  copier.  I  know  this  by  a  test 
which  has  often  served  me.  I  use  the  subjunctive — 'if  no  man 


352  A  BUDGET  OF  PARADOXES. 

have  done  nothing,'  an  ordinary  transcriber,  narrating  a  quotation 
almost  always  lets  his  own  habit  write  has.  The  fourth  extract 
has  three  alterations,  all  tending  to  make  me  ridiculous.  None 
is  altered,  in  two  places,  into  nine,  denial  into  decimal,  and  comes 
into  aims ;  so  that  '  none,  the  denial  of  one,  comes  to  be  asso- 
ciated with  the  denial  of  plurality,'  reads  as  '  nine,  the  decimal 
of  one,  aims  to  be  associated  with  the  decimal  of  plurality.'  This 
is  intentional  ;  had  it  been  a  compositor's  reading  of  bad  hand- 
writing, these  would  not  have  been  the  only  mistakes  ;  to  say 
nothing  of  the  corrector  of  the  press.  And  both  the  compositor 
and  reader  would  have  guessed,  from  the  first  line  being  trans- 
lated into  '  one  is  not  one,'  that  it  must  have  been  '  one's  none,' 
not  '  one's  nine.'  But  it  was  not  intended  that  the  gem  should 
be  recovered  from  the  unfathomed  cave,  and  set  in  a  Budget  of 
Paradoxes. 

We  have  had  plenty  of  slander-paradox.  I  now  give  a  halfpenny- 
worth of  bread  to  all  this  sack,  an  instance  of  the  paradox  of 
benevolence,  in  which  an  individual  runs  counter  to  all  the 
ideas  of  his  time,  and  sees  his  way  into  the  next  century.  At 
Amiens,  at  the  end  of  the  last  century,  an  institution  was  en- 
dowed by  a  M.  de  Morgan,  to  whom  I  hope  I  am  of  kin,  but  I 
cannot  trace  it ;  the  name  is  common  at  Amiens.  It  was  the 
first  of  the  kind  I  ever  heard  of.  It  is  a  Salle  d'Asyle  for 
childen,  who  are  taught  and  washed  and  taken  care  of  during 
the  hours  in  which  their  parents  must  be  at  work.  The  founder 
was  a  large  wholesale  grocer  and  colonial  importer,  who  was 
made  a  Baron  by  Napoleon  I.  for  his  commercial  success  and  his 
charities. 


1862.  Mr.  Smith  replies  to  me,  still  signing  himself  Nauticus  : 
I  give  an  extract : — 

'  By  hypothesis  [what,  again  !]  let  14°  24'  be  the  chord  of  an  arc  of 
15°  [but  I  wont,  says  14°  24'],  and  consequently  equal  to  a  side  of  a 
regular  polygon  of  24  sides  inscribed  in  the  circle.  Then  4  times 
14°  24'  =  57°  36'  =  the  radius  of  the  circle  .  .  .' 

That  is,  four  times  the  chord  of  an  arc  is  the  chord  of  four  times 
the  arc  :  and  the  sum  of  four  sides  of  a  certain  pentagon  is  equal 
to  the  fifth.  This  is  the  capital  of  the  column,  the  crown  of  the 
arch,  the  apex  of  the  pyramid,  the  watershed  of  the  elevation. 
Oh !  J.  S. !  J.  S.  !  groans  Greometry — Summum  J>  S.  summa 


THE   TWO   J.  S'S.  853 

injuria !  The  other  J.  S.,  Joseph  Scaliger,  as  already  mentioned, 
had  his  own  way  of  denying  that  a  straight  line  is  always  the 
shortest  distance  between  two  points.  A  parallel  might  be  insti- 
tuted, but  not  in  half  a  column.  And  J.  S.  the  second  has  been 
so  tightly  handled  that  he  may  now  be  dismissed,  with  an  inscrip- 
tion for  his  circular  shield,  obtained  by  changing  Lexica  contexat 
into  Circus  quadrandus  in  an  epigram  of  J.  S.  the  first :  — 

Si  quern  dura  manet  sententia  judicis,  olim 

Damnatum  serumnis  suppliciisque  caput, 

Hunc  neque  fabrili  lassent  ergastula  massa, 

Nee  rigidas  vexent  fossa  metalla  manus. 

Circus  quadrandus  :  nam — caetera  quid  moror  ? — omnes 

Pcenarum  facies  hie  labor  unus  habet. 

I  had  written  as  far  as  damnatum  when  in  came  the  letter  of 
Nauticus  as  a  printed  slip,  with  a  request  that  I  would  consider 
the  slip  as  a  '  revised  copy.'  Not  a  word  of  alteration  in  the 
part  I  have  quoted  I  And  in  the  evening  came  a  letter  desiring 
that  I  would  alter  a  gross  error ;  but  not  the  one  above  :  this 
is  revising  without  revision  I  If  there  were  cyclometers  enough 
of  this  stamp,  they  would,  as  cultivation  progresses — and  really, 
with  John  Stuart  Mill  in  for  Westminster,  it  seems  on  the  move, 
even  though,  as  I  learn  while  correcting  the  proof,  Gladstone  be 
out  from  Oxford  ;  for  Oxford  is  no  worse  than  in  1829,  while 
Westminster  is  far  above  what  she  ever  has  been  :  election  time 
excuses  even  such  a  parenthesis  as  this — be  engaged  to  amuse 
those  who  can  afford  it  with  paralogism  at  their  meals,  after  the 
manner  of  the  other  jokers  who  wore  the  caps  and  bells.  The 
rich  would  then  order  their  dinners  with  panem  et  Gircenses, — up 
with  the  victuals  and  the.  circle-games — as  the  poor  did  in  the 
days  of  old. 

Mr.  Smith  is  determined  that  half  a  column  shall  not  do. 
Not  a  day  without  something  from  him  :  letter,  printed  proof, 
pamphlet.  In  what  is  the  last  at  this  moment  of  writing  he  tells 
me  that  part  of  the  title  of  a  work  of  his  will  be  '  Professor  De 
Morgan  in  the  pillory  without  hope  of  escape.'  And  where  will 
he  be  himself  ?  This  I  detected  by  an  effort  of  reasoning  which 
I  never  could  have  made  except  by  following  in  his  steps.  In  all 
matters  connected  with  TT  the  letters  /  and  g  are  closely  related : 
tins  appears  in  the  well-known  formula  for  the  time  of  oscillation, 
TT  %/(£ :  g}.  Hence  g  may  be  written  for  £,  but  only  once  :  do  it 
twice,  and  you  require  the  time  to  be  TT  */  (I*  :  gr2).  This  may  be 
reinforced  by  observing  that  if  as  a  datum,  or  if  you  dislike  that 

A  A 


354  A  BUDGET   OF  PAEADOXES. 

word,  by  hypothesis,  the  first  I  be  a  g,  it  is  absurd  that  it  should 
be  an  I.  Write  g  for  the  first  I,  and  we  have  un  fait  accompli. 
I  shall  be  in  pillory ;  and  overhead,  in  a  cloud,  will  sit  Mr.  James 
Smith  on  one  stick  laid  across  two  others,  under  a  nimbus  of  3£ 
diameters  to  the  circumference — in  7r-glory.  Oh  for  a  drawing 
of  this  scene !  Mr.  De  Morgan  presents  his  compliments  to 
Mr.  James  Smith,  and  requests  the  honour  of  an  exchange  of 
photographs. 

July  26. — Another  printed  letter. — Mr.  James  Smith  begs  for 
a  distinct  answer  to  the  following  plain  question  :  *  Have  I  not 
in  this  communication  brought  under  your  notice  truths  that 
were  never  before  dreamed  of  in  your  geometrical  and  mathe- 
matical philosophy  ? '  To  which,  he  having  taken  the  precaution 
to  print  the  word  truths  in  italics,  I  can  conscientiously  answer, 
Yes,  you  have.  And  now  I  shall  take  no  more  notice  of  these 
truths,  until  I  receive  something  which  surpasses  all  that  has  yet 
been  done. 


The  Circle  secerned  from  the  Square  ;  and  its  area  gauged  in 
terms  of  a  triangle  common  to  both.  By  Wm.  Houlston,  Esq. 
London  and  Jersey,  1862, 4to. 

Mr.  Houlston  squares  at  about  four  poetical  quotations  in  a 
page,  and  brings  out  7r==  3-14213  ....  His  forntispieee  is  a 
variegated  diagram,  having  parts  designated  Inigo  and  Outigo. 
All  which  relieves  the  subject,  but  does  not  remove  the  error. 

Considerations  respecting  the  figure  of  the  Earth  .  .  .  By  C.  F. 
Bakewell.  London,  1862.  8vo. 

Newton  and  others  think  that  in  a  revolving  sphere  the  loose 
surface  matter  will  tend  to  the  equator  :  Mr.  Bakewell  thinks  it 
will  tend  to  the  poles. 

On  eccentric  and  centric  force  :  a  new  theory  of  projection.  By 
H.  F.  A.  Pratt,  M.D.  London,  1862,  8vo. 

Dr.  Pratt  not  only  upsets  Newton,  but  cuts  away  the  very 
ground  he  stands  on  :  for  he  destroys  the  first  law  of  motion, 
and  will  not  have  the  natural  tendency  of  matter  in  motion  to  be 
rectilinear.  This,  as  we  have  seen,  was  John  Walsh's  notion.  In 
a  more  recent,  wprk  '  On  Orbital  Motion,'  London,  1863,  8vo., 
Dr.  Pratt  insists  on  another  of  Walsh's  notions,  namely,  that  the 
precession  of  the  equinoxes  is  caused  by  the  motion  of  the  solar 


BIRKS  ON  MATTER  AND   ETHER. 

system  round  a  distant  central  sun.  In  this  last  work  the  author 
refers  to  a  few  notes,  which  completely  destroy  the  theory  of 
gravitation  in  terms  '  perfectly  intelligible  as  well  to  the  un- 
learned as  to  the  learned ' :  to  me  they  are  quite  unintelligible, 
which  rather  tends  to  confirm  a  notion  I  have  long  had,  that  I 
am  neither  one  thing  nor  the  other.  There  is  an  ambiguity 
of  phrase  which  delights  a  writer  on  logic,  always  on  the  look  out 
for  specimens  of  homonymia  or  cequivocatio.  The  author,  as  a 
physician,  is  accustomed  to  '  appeal  from  mere  formulae ' :  accord- 
ingly, he  sets  at  nought  the  whole  of  the  mathematics,  which  he 
does  not  understand.  This  equivocation  between  the  formula  of 
the  physician  and  that  of  the  mathematician  is  as  good,  though 
not  so  perceptible  to  the  world  at  large,  as  that  made  by  Mr. 
Briggs's  friend  in  Punch's  picture,  which  I  cut  out  to  paste  into  my 
Logic.  Mr.  Briggs  wrote  for  a  couple  of  bruisers,  meaning  to 
prepare  oats  for  his  horses :  his  friend  sent  him  the  Whitechapel 
Chicken  and  the  Bayswater  Slasher,  with  the  gloves,  all  ready. 

On  matter  and  ether,  and  the  secret  laws  of  physical  change.  By 
T.  R.  Birks,  M.A.  Cambridge,  1862,  8vo. 

Bold  efforts  are  made  at  molecular  theories,  and  the  one  before 
me  is  ably  aimed.  When  the  Newton  of  this  subject  shall  be 
seated  in  his  place,  books  like  the  present  will  be  sharply  looked 
into,  to  see  what  amount  of  anticipation  they  have  made. 

The  history  of  the  '  thorn  tree  and  bush  '  from  the  earliest  to  the 
present  time  :  in  which  is  clearly  and  plainly  shown  the  descent 
of  her  most  gracious  Majesty  and  her  Anglo-Saxon  people  from 
the  half  tribe  of  Ephraim,  and  possibly  from  the  half  tribe  of 
Manasseh  ;  and  consequently  her  right  and  title  to  possess,  at 
the  present  moment,  for  herself  and  for  them,  a  share  or  shares 
of  the  desolate  cities  and  places  in  the  land  of  their  forefathers  ! 
By  Theta,  M.D.  (Private  circulation.)  London,  1862,  8vo. 

This  is  much  about  Thorn,  and  its  connected  words,  Thor, 
Thoth,  Theta,  &c.  It  is  a  very  mysterious  vagary.  The  author 
of  it  is  the  person  whom  I  have  described  elsewhere  as  having 
for  his  device  the  round  man  in  the  three-cornered  hole,  the 
writer  of  the  little  heap  of  satirical  anonymous  letters  about  the 
Beast  and  666.  By  accident  I  discovered  the  writer :  so  that  if 
there  be  any  more  thorns  to  crackle  under  the  pot,  they  need  not 
be  anonymous. 

Nor  will  they  be  anonymous.  Since  I  wrote  the  above,  I  have 
received  onymous  letters,  as  ominous  as  the  rest.  The  writer, 

A  A  2 


856  A  BUDGET  OF  PARADOXES. 

William  Thorn,  M.D.,  is  obliged  to  reveal  himself,  since  it  is  his 
object  to  prove  that  he  himself  is  one  666.  By  using  W  for  a 
double  Vau  (or  12)  he  cooks  the  number  out  of  his  own  name. 
But  he  says  it  is  the  number  not  of  a  beast  but  of  a  man,  and 
adds,  '  Thereby  hangs  a  tale ! '  which  sounds  like  contradiction. 
He  informs  me  that  he  will  talk  the  matter  over  with  me :  but  I 
shall  certainly  have  nothing  to  say  to  a  gentleman  of  his  number ; 
it  is  best  to  keep  on  the  safe  side. 

In  one  letter  I  am  informed  that,  not  a  line  should  I  have  had, 
but  for  my  '  sneer  at  666,'  which,  therefore,  I  am  well  pleased  to 
have  given.  I  am  also  told  that  my  name  means  the  '  "  garden 
of  death,"  that  place  in  which  the  tree  of  knowledge  was  plucked, 
and  so  you  are  like  your  name  "  dead  "  to  the  fact  that  you  are 
an  Israelite,  like  those  in  Ezekiel  37  ch.'  Some  hints  are  given 
that  I  shall  not  fare  well  in  the  next  world,  which  anyone  who 
reads  the  chapter  in  Ezekiel  will  see  is  quite  against  his  com- 
parison. The  reader  must  not  imagine  that  my  prognosticator 
means  Morgan  to  be  a  corruption  of  Mortjardin ;  he  proves  his 
point  by  Hebrew :  but  any  philologist  would  tell  him  the  true 
derivation  of  the  name,  and  how  Glamorgan  came  to  get  it.  It 
will  be  of  much  comfort  to  those  young  men  who  have  not  got 
through  to  know  that  the  tree  of  knowledge  itself  was  once  in  the 
same  case.  And  so  good  bye  to  666  for  the  present,  and  the 
assumption  that  the  enigma  is  to  be  solved  by  the  united 
numeral  forces  of  the  letters  of  a  word. 

It  is  worthy  of  note  that,  as  soon  as  my  Budget  commenced, 
two  guardian  spirits  started  up,  fellow  men  as  to  the  flesh,  both 
totally  unknown  to  me :  they  have  stuck  to  me  from  first  to  last. 
James  Smith,  Esq.,  finally  Nauticus,  watches  over  iny  character 
in  this  world,  and  would  fain  preserve  me  from  ignorance,  folly, 
and  dishonesty,  by  inclosing  me  in  a  magic  circle  of  3|  diameters 
in  circumference.  The  round  man  in  the  three-cornered  hole, 
finally  William  Thorn,  M.D.  takes  charge  of  my  future  destiny, 
and  tries  to  bring  me  to  the  truth  by  unfolding  a  score  of  meanings 
— all  right — of  666.  He  hints  that  I,  and  my  wife,  are  servants 
of  Satan :  at  least  he  desires  us  both  to  remember  that  we  cannot 
serve  (rod  and  Satan ;  and  he  can  hardly  mean  that  we  are 
serving  the  first,  and  that  he  would  have  us  serve  the  second. 
As  becomes  an  interpreter  of  the  Apocalypse,  he  uses  seven 
different  seals  ;  but  not  more  than  one  to  one  letter.  If  his 
seals  be  all  signet-rings,  he  must  be  what  Aristophanes  calls  a 
sphragidonychargocometical  fellow.  But — and  many  thanks  to 
him  for  the  same — though  an  M.D.,  he  has  not  sent  me  a  single 


DR.   THORN — MR.   BIDKX.  357 

vial.  And  so  much  for  my  tree  of  secular  knowledge  and  my 
tree  of  spiritual  life  :  I  dismiss  them  with  thanks  from  myself 
and  thanks  from  my  reader.  The  dual  of  the  Pythagorean 
system  was  Isis  and  Diana ;  of  the  Jewish  law,  Moses  and  Aaron ; 
of  the  City  of  London,  Grog  and  Magog ;  of  the  Paradoxiad, 
James  Smith,  Esq.,  and  William  Thorn,  M.D. 

September,  1866.  Mr.  James  Biden  has  favoured  me  with 
some  of  his  publications.  He  is  a  rival  of  Dr.  Thorn  ;  a  prophet 
by  name-right  and  crest-right.  He  is  of  royal  descent  through 
the  De  Bidun's.  He  is  the  watchman  of  Ezekiel :  God  has  told 
him  so.  He  is  the  author  of  The  True,  Church,  a  phrase  which 
seems  to  have  a  book-meaning  and  a  mission-meaning.  He  shall 
speak  for  himself: — 

'  A  crest  of  the  Bidens  has  significance.  It  is  a  lion  rampant 
between  wing — swings  in  Scripture  denote  the  flight  of  time. 
Thus  the  beasts  or  living  creatures  of  the  Revelations  have  each 
six  wings,  intimating  a  condition  of  mankind  up  to  and  towards 
the  close  of  six  thousand  years  of  Bible  teaching.  The  two  wings 
of  the  crest  would  thus  intimate  power  towards  the  expiration  of 
2000  years,  as  time  is  marked  in  the  history  of  Great  Britain, 

'  In  a  recent  publication,  The  Pestilence,  Why  Inflicted,  are 
given  many  reasons  why  the  writer  thinks  himself  to  be  the 
appointed  watchman  foretold  by  Ezekiel,  chapters  iii.  and  xxxiii. 
Among  the  reasons  are  many  prophecies  fulfilled  in  him.  Of 
these  it  is  now  needful  to  note  two  as  bearing  especially  on  the 
subject  of  the  reign  of  Darius. 

4  1. — In  Daniel  it  is  said,  '  Darius  the  Median  took  the  kingdom, 
being  about  threescore  and  two  years  old." — Daniel  v.  31. 

'  When  "Belshazzar"  the  king  of  the  Chaldeans  is  found  wanting, 
Darius  takes  the  kingdom.  It  is  not  given  him  by  the  popular 
voice ;  he  asserts  his  right,  and  this  is  not  denied.  He  takes  it 
when  about  sixty-two  years  of  age.  The  language  of  Daniel  is 
prophetic,  and  Darius  has  in  another  an  antitype.  The  writer 
was  born  July  18th,  1803  ;  and  the  claim  was  asserted  at  the 
close  of  1865,  when  he  was  about  sixty-two  years  of  age. 

'The  claims  which  have  been  asserted  demand  a  settled  faith, 
and  which  could  only  be  reached  through  a  long  course  of  divine 
teaching.' 

When  I  was  a  little  boy  at  school,  one  of  my  schoolfellows  took 
it  into  his  head  to  set  up  a  lottery  of  marbles :  the  thing  took, 
and  he  made  a  stony  profit.  Soon,  one  after  another,  every  boy 


858  A  BUDGET   OF  PARADOXES. 

had  his  lottery,  and  it  was,  <I  won't  put  into  yours  unless  you 
put  into  mine.'  This  knocked  up  the  scheme.  It  will  be  the 
same  with  the  prophets.  Dr.  Thorn,  Mr.  Biden,  Mrs.  Cottle,  &c. 
will  grow  imitators,  until  we  are  all  pointed  out  in  the  Bible  : 
but  A  will  not  admit  B's  claim  unless  B  admits  his.  For  myself, 
as  elsewhere  shown,  I  am  the  first  Beast  in  the  Eevelations. 

Every  contraband  prophet  gets  a  few  followers :  it  is  a  great 
point  to  make  these  sequacious  people  into  Buridan's  asses,  which 
they  will  become  when  prophets  are  so  numerous  that  there  is  no 
choosing. 

An  historical  survey  of  the  Astronomy  of  the  Ancients.     By  the 
Bt.  Hon.  Sir  G.  C.  Lewis.     8vo.  1862. 

There  are  few  men  of  our  day  whom  I  admire  more  than  the 
late  Sir  Gr.  Lewis :  he  was  honest,  earnest,  sagacious,  learned,  and 
industrious.  He  probably  sacrificed  his  life  to  his  conjunction  of 
literature  and  politics :  and  he  stood  high  as  a  minister  of  state 
in  addition  to  his  character  as  a  man  of  letters.  The  work  above 
named  is  of  great  value,  and  will  be  read  for  its  intrinsic  merit, 
consulted  for  its  crowd  of  valuable  references,  quoted  for  its  aid 
to  one  side  of  many  a  discussion,  and  opposed  for  its  force  against 
the  other.  Its  author  was  also  a  wit  and  a  satirist.  I  know  of 
three  classical  satires  of  our  day  which  are  inimitable  imitations : 
Mr.  Maiden's  Pragmatized  Legends,  Mr.  Mansel's  Phrontisterion, 
and  Sir  Gr.  Cornewall  Lewis's  Inscriptio  Antiqua.  In  this  last, 
IIEYDIDDLEDIDDLETHECATANDTHEFIDDLE  &c.  is  treated  as  an  Oscan 
inscription,  and  rendered  into  Latin  by  approved  methods.  As 
few  readers  have  seen  it,  I  give  the  result : — 

'  Hejus  dedit  libenter,  dedit  libenter.  Deus  propitius  [est],  deus 
[donatori]  libenter  favet.  Deus  in  viarum  junctura  ovoruna  dape 
[colitur],  deus  mundi.  Deus  in  litatione  voluit,  benigno  animo, 
hsedurn,  taurum  intra  fines  [loci  sacri]  portandos.  Deus,  bis  lustratus, 
beat  fossam  sacree  libationis.' 

How  then  comes  the  history  of  astronomy  among  the  paradoxes  ? 
Simply  because  the  author,  so  admirable  when  writing  about  what 
he  knew,  did  not  know  what  he  did  not  know,  and  blundered  like 
a  circle-squarer.  And  why  should  the  faults  of  so  good  a  writer 
be  recorded  in  such  a  list  as  the  present  ?  For  three  reasons : 
First,  and  foremost,  because  if  the  exposure  be  not  made  by  some 
one,  the  errors  will  gradually  ooze  out,  and  the  work  will  get  the 
character  of  inaccurate.  Nothing  hurts  a  book  of  which  few  can 
fathom  the  depths  so  much  as  a  plain  blunder  or  two  on  the 
surface.  Secondly,  because  the  reviews  either  passed  over  these 


SIR    G.   C.  LEWIS.  359 

errors  or  treated  them  too  gently,  rather  implying  their  existence 
than  exposing  them.  Thirdly,  because  they  strongly  illustrate 
the  melancholy  truth,  that  no  one  knows  enough  to  write  about 
what  he  does  not  know.  The  distinctness  of  the  errors  is-  a  merit ; 
it  proceeds  from  the  clear-headedness  of  the  author.  The  sup- 
pression in  the  journals  may  be  due  partly  to  admiration  of  the 
talent  and  energy  which  lived  two  difficult  lives  at  once,  partly 
to  respect  for  high  position  in  public  affairs,  partly  to  some  of  the 
critics  being  themselves  men  of  learning  only,  unable  to  detect 
the  errors.  But  we  know  that  action  and  reaction  are  equal  and 
contrary.  If  our  generation  take  no  notice  of  defects,  and  allow 
them  to  go  down  undetected  among  merits,  the  next  generation 
will  discover  them,  will  perhaps  believe  us  incapable  of  detecting 
them,  at  least  will  pronounce  our  judgment  good  for  nothing, 
and  will  form  an  opinion  in  which  the  merits  will  be  underrated : 
so  it  has  been,  is,  and  will  be.  The  best  thing  that  can  be  done 
for  the  memory  of  the  author  is  to  remove  the  unsound  part  that 
the  remainder  may  thrive.  The  errors  do  not  affect  the  work  ; 
they  occur  in  passages  which  might  very  well  have  been  omitted  : 
and  I  consider  that,  in  making  them  conspicuous,  I  am  but  cutting 
away  a  deleterious  fungus  from  a  noble  tree. 

(P.  154).  The  periodic  times  of  the  five  planets  were  stated  by 
Eudoxus,  as  we  learn  from  Simplicius ;  the  following  is  his  statement, 
to  which  the  true  times  are  subjoined,  for  the  sake  of  comparison : — 

Statement  of  Eudoxus.  True  time. 

Mercury  ...  1  year  ....  —  87d.  23h. 
Venus  ....  1  „  ....  -  224d.  16h. 
Mars  ....  2  „  .  .  .  .  ly.  321d.  23h. 
Jupiter  ...  12  „  ....  lly.  315d.  14h. 
Saturn  ....  30  , 29y.  174d.  Ih. 

Upon  this  determination  two  remarks  may  be  made.  First,  the  error 
with  respect  to  Mercury  and  Venus  is  considerable ;  with  respect  to 
Mercury,  it  is,  in  round  numbers,  365  instead  of  88  days,  more  than 
four  times  too  much.  Aristotle  remarks  that  Eudoxus  distinguishes 
Mercury  and  Venus  from  the  other  three  planets  by  giving  them  one 
sphere  each,  with  the  poles  in  common.  The  proximity  of  Mercury  to 
the  sun  would  render  its  course  difficult  to  observe  and  to  measure, 
but  the  cause  of  the  large  error  with  respect  to  Venus  (130  days)  is 
not  apparent. 

Sir  Cr.  Lewis  takes  Eudoxus  as  making  the  planets  move  round 
the  sun ;  he  has  accordingly  compared  the  geocentric  periods  of 
Eudoxus  with  our  heliocentric  periods.  What  greater  blunder  can 
be  made  by  a  writer  on  ancient  astronomy  than  giving  Eudoxus 


360  A   BUPGET   OF  PARADOXES. 

the  Copernican  system  ?     If  Mercury  were  a  black  spot  in  the 
middle  of  the  sun  it  would  of  course  move  round  the  earth  in  a  year, 
or  appear  to  do  so :  let  it  swing  a  little  on  one  side  and  the  other 
of  the  sun,  and  the  average  period  is  still  a  year,  with  slight 
departures  both  ways.     The   same   for   Venus,  with  larger   de- 
partures.    Say  that  a  person  not  much  accustomed  to  the  distinc- 
tion might  for  once  write  down  the  mistake  ;   how  are  we  to 
explain  its  remaining  in  the  mind  in  a  permanent  form,  and 
being  made  a  ground  for  such  speculation  as  that  of  the  difficulty 
of  observing  Mercury  leading  to  a  period  four  times  what  it  ought 
to  be,  corrected  in  proof  and  published  by  an  industrious  and 
thoughtful  person  ?     Only  in  one  way  :  the  writer  was  quite  out 
of  his  depth.     This  one  case  is  conclusive  ;  be  it  said  with  all 
respect  for  the  real  staple  of  the  work  and  of  the  author.     He 
knew  well  the  difference  of  the  systems,  but  not  the  effect  of  the 
difference  :  he  is  another  instance  of  what  I  have  had  to  illustrate 
by  help  of  a  very  different  person,  that  it  is  difficult  to  reason 
well  upon  matter  which  is  not  familiar. 

(P.  254).  Copernicus,  in  fact,  supposed  the  axis  of  the  earth  to 
be  always  turned  towards  the  Sun.  U69°  [(169).  See  Delambre, 
Hist.  Astr.  Mod.  vol.  i.  p.  96].  It  was  reserved  to  Kepler  to  pro- 
pound the  hypothesis  of  the  constant  parallelism  of  the  earth's  axis 
to  itself. 

If  there  be  one  thing  more  prominent  than  another  in  the 
work  of  Copernicus  himself,  in  the  popular  explanations  of  it, 
and  in  the  page  of  Delambre  cited,  it  is  that  the  parallelism  of 
the  earth's  axis  is  a  glaring  part  of  the  theory  of  Copernicus. 
What  Kepler  did  was  to  throw  away,  as  unnecessary,  the  method 
by  which  Copernicus,  per  fas  et  nefas,  secured  it.  Copernicus, 
thinking  of  the  earth's  orbital  revolution  as  those  would  think 
who  were  accustomed  to  the  solid  orbs — and  much  as  the  stoppers 
of  the  moon's  rotation  do  now  :  why  do  they  not  strengthen  them- 
selves with  Copernicus? — thought  that  the  earth's  axis  would 
always  incline  the  same  end  towards  the  sun,  unless  measures 
were  taken  to  prevent  it.  He  did  take  measures  :  he-  invented  a 
compensating  conical  motion  of  the  axis  to  preserve  the  parallel- 
ism; and,  which  is  one  of  the  most  remarkable  points  of  his 
system,  he  obtained  the  precession  of  the  equinoxes  by  giving 
the  necessary  trifle  more  than  compensation.  What  stares  us  in 
the  face  at  the  beginning  of  the  paragraph  to  which  the  author 
refers  ? 


SIR   G.   0.   LEWIS.  361 

'  C'est  done  ponr  arriver  a  ce  parallelisme,  on  ponr  le  conserrer,  qne 
Copemic  a  cm  devoir  recourir  a  ce  mouvement  egal  et  oppose  qui 
detruit  1'effet  qu'il  attribue  si  gratuitement  au  premier,  de  deranger  le 
parallelisme.' 

Parallelism  at  any  price,  is  the  motto  of  Copernicus  :  you  need 
not  pay  so  dear,  is  the  remark  of  Kepler. 

The  opinions  given  by  Sir  G.  Lewis  about  the  effects  of  modern 
astronomy,  which  he  does  not  understand  and  singularly  under- 
values, will  now  be  seen  to  be  of  no  authority.    He  fancies  that  — 
to  give  an  instance  —  for  the  determination  of  a  ship's  place,  the 
invention  of  chronometers  has  been  far  more  important  than  any 
improvement  in  astronomical  theory  (p.  254).     Not  to  speak  of 
latitude,  —  though  the  omission  is  not  without  importance,  —  he 
ought  to  have  known  that  longitude  is  found  by  the  difference 
between  what  o'clock  it  is  at  Greenwich  and  at  the  ship's  place, 
at  one  absolute  moment  of  time.     Now  if  a  chronometer  were 
quite  perfect  —  which  no  chronometer  is,  be  it  said  —  and  would 
truly  tell  Greenwich  mean  time  all  over  the  world,  it  ought  to 
have  been  clear  that  just  as  good  a  watch  is  wanted  for  the  time 
at  the  place  of  observation,  before  the  longitude  of  that  place 
with  respect  to  Greenwich  can  be  found.     There  is  no  such  watch, 
except  the  starry  heaven  itself:  and  that  watch  can  only  be  read 
by  astronomical  observation,  aided  by  the  best  knowledge  of  the 
heavenly  motions. 

I  think  I  have  done  Sir  G.  Lewis's  very  excellent  book  more 
good  than  all  the  reviewers  put  together. 

I  will  give  an  old  instance  in  which  literature  got  into  con- 
fusion about  astronomy.  Theophrastus,  who  is  either  the  culprit 
or  his  historian,  attributes  to  Meton,  the  contriver  of  the  lunar 
calendar  of  nineteen  years,  which  lasts  to  this  day,  that  his 
solstices  were  determined  for  him  by  a  certain  Phaeinus  of  Elis 
on  Mount  Lycabettus.  Nobody  else  mentions  this  astronomer  : 
though  it  is  pretty  certain  that  Meton  himself  made  more  than 
one  appointment  with  him  for  the  purpose  of  observing  solstices  ; 
and  we  may  be  sure  that  if  either  were  behind  his  time,  it  was 
Meton.  For  Phaeinus  Helius  is  the  shining  sun  himself;  and  in 
the  astronomical  poet  Aratus  we  read  about  the  nineteen  years  of 
the  shining  sun  — 

<f>acirov  ijtXloio. 


Some  man  of  letters  must  have  turned  Apollo  into  Phaeinus  of 
Elis  ;  and  there  he  is  in  the  histories  of  astronomy  to  this  day. 


362  A  BUDGET   OF  PAEADOXES. 

Salmasius  will  have  Aratus  to  have  meant  him,  and  proposes  to 
read  rjXsLoio  :  he  did  not  observe  that  Phaeinus  is  a  very  common 
adjective  of  Aratus,  and  that,  if  his  conjecture  were  right,  this 
Phaeinus  would  be  the  only  non-mythical  man  in  the  poems  of 
Aratus. 

[When  I  read  Sir  Greorge  Lewis's  book,  the  points  which  I  have 
criticised  struck  me  as  not  to  be  wondered  at,  but  I  did  not 
remember  why  at  the  time.  A  Chancellor  of  the  Exchequer  and 
a  writer  on  ancient  astronomy  are  birds  of  such  different  trees 
that  the  second  did  not  recal  the  first.  In  1855  I  was  one  of  a 
deputation  of  about  twenty  persons  who  waited  on  Sir  Or.  Lewis, 
as  Chancellor  of  the  Exchequer,  on  the  subject  of  the  decimal 
coinage.  The  deputation  was  one  of  much  force :  Mr.  Airy,  with 
myself  and  others,  represented  mathematics ;  William  Brown, 
whose  dealings  with  the  United  States  were  reckoned  by  yearly 
millions,  counted  duodecimally  in  England  and  decimally  in 
America,  was  the  best,  but  not  the  only,  representative  of  com- 
merce. There  were  bullionists,  accountants,  retailers,  &c.  Sir 
Gr.  L.  walked  into  the  room,  took  his  seat,  and  without  waiting 
one  moment,  began  to  read  the  deputation  a  smart  lecture  on  the 
evils  of  a  decimal  coinage  ;  it  would  require  alteration  of  all  the 
tables,  it  would  impede  calculation,  &c.  &c.  Of  those  arguments 
against  it  which  weighed  with  many  of  better  knowledge  than 
his,  he  obviously  knew  nothing.  The  members  of  the  deputation 
began  to  make  their  statements,  and  met  with  curious  denials. 
He  interrupted  me  with  '  Surely  there  is  no  doubt  that  the 
calculations  of  our  books  of  arithmetic  are  easier  than  those  in 
the  French  books.'  He  was  not  aware  that  the  universally 
admitted  superiority  of  decimal  calculation  made  many  of  those 
who  prefer  our  system  for  the  market  and  the  counter  cast  a 
longing  and  lingering  look  towards  decimals.  My^answer  and 
the  smiles  which  he  saw  around,  made  him  give  a  queer  puzzled 
look,  which  seemed  to  say,  '  I  may  be  out  of  my  depth  here ! ' 
His  manner  changed,  and  he  listened.  I  saw  both  the  slap-dash 
mode  in  which  he  dealt  with  subjects  on  which  he  had  not 
thought,  and  the  temperament  which  admitted  suspicion  when 
the  means  of  knowledge  came  in  his  way.  Having  seen  his  two 
phases,  I  wonder  neither  at  his  more  than  usual  exhibition  of 
shallowness  when  shallow,  nor  at  the  intensity  of  the  contrast 
when  he  had  greater  depth.] 

Among  the  paradoxers  are  the  political  paradoxers  who  care 
not  how  far  they  go  in  debate,  their  only  object  being  to  carry 
the  House  with  them  for  the  current  evening.  What  I  have  said 


DECIMAL   COINAGE.  363 

of  editors  I  repeat  of  them.  The  preservation  of  a  very  marked 
instance,  the  association  of  political  recklessness  with  cyclo- 
metrical  and  Apocalyptic  absurdity,  may  have  a  tendency  to  warn, 
not  indeed  any  hardened  publicman  and  sinner,  but  some  young 
minds  which  have  yearnings  towards  politics,  and  are  in  formation 
of  habits. 

In  the  debate  on  decimal  coinage  of  July  12,  1855,  Mr.  Lowe, 
then  member  for  Kidderminster,  an  effective  speaker  and  a  smart 
man,  exhibited  himself  in  a  speech  on  which  I  wrote  a  comment 
for  the  Decimal  Association.  I  have  seldom  seen  a  more  wretched 
attempt  to  distort  the  points  of  a  public  question  than  the  whole 
of  this  speech.  Looking  at  the  intelligence  shown  by  the  speaker 
on  other  occasions,  it  is  clear  that  if  charity,  instead  of  believing 
all  things,  believed  only  all  things  but  one,  he  might  tremble  for 
his  political  character ;  for  the  honesty  of  his  intention  on  this 
occasion  might  be  the  incredible  exception.  I  give  a  few  para- 
graphs, with  the  comments  : — 

'  In  commenting  on  the  humorous,  but  still  argumentative  speech 
of  Mr.  Lowe,  the  member  for  Kidderminster,  we  may  observe,  in 
general,  that  it  consists  of  points  which  have  been  several  times  set 
forth,  and  several  times  answered.  Mr.  Lowe  has  seen  these  answers, 
but  does  not  allude  to  them,  far  less  attempt  to  meet  them.  There 
are,  no  doubt,  individuals,  who  show  in  their  public  speaking  the 
outward  and  visible  signs  of  a  greater  degree  of  acuteness  than  they 
can  summon  to  guide  their  private  thinking.  If  Mr.  Lowe  be  not  one 
of  these,  if  the  power  of  his  mind  in  the  closet  be  at  all  comparable  to 
the  power  of  his  tongue  in  the  House,  it  may  be  suspected  that  his 
reserve  with  respect  to  what  has  been  put  forward  by  the  very  parties 
against  whom  he  was  contending,  arises  from  one  or  both  of  two 
things — a  high  opinion  of  the  arguments  which_  he  ignored — a  low 
opinion  of  the  generality  of  the  persons  whom  he  addressed.  [Both, 
I  doubt  not]. 

"  Did  they  calculate  in  florins  ?  "     In  the  name  of  common  sense, 

how  can  it  be  objected  to  a  system 

that  people  do  not  use  it  before  it  is  introduced  ?  Let  the  decimal 
system  be  completed,  and  calculation  shall  be  made  in  florins ;  that  is, 
florins  shall  take  their  proper  place.  If  florins  were  introduced  now, 
there  must  be  a  column  for  the  odd  shilling. 

"  He  was  glad  that  some  hon.  If  the  hon.  gentleman  make 
gentleman  had  derived  benefit  this  assertion  of  himself,  it  is  not 
from  the  issue  of  florins.  His  for  us  to  gainsay  it.  It  only- 
only  experience  of  their  conve-  proves  that  he  is  one  of  that 
nience  was,  that  when  he  ought  class  of  men  who  are  described 
to  have  received  half-a-crown,  he  in  the  old  song,  of  which  ono 


364  A   BUDGET   OF   PARADOXES. 

had   generally  received  a  florin,        couplet  runs  thus  :— 
and  when  he  ought  to  have  paid       I  sold  my  cow  to  buy  me  a  calf; 
a  florin,  he   had  generally   paid        I  never  make  a  bargain  but  I  lose 
half-a-crown."     (Hear,  hear,  and  half, 

laughter.)  With  a  &c.  &c.  &c. 

But  he  cannot  mean  that  Englishmen  in  general  are  so  easily 
managed.  And  as  to  Jonathan,  who  is  but  John  lengthened  out  a 
little,  he  would  see  creation  whittled  into  chips  before  he  would  even 
split  what  may  henceforth  be  called  the  Kidderminster  difference. 
The  House,  not  unmoved — for  it  laughed — with  sly  humour  decided 
that  the  introduction  of  the  florin  had  been  "  eminently  successful  and 
satisfactory." 

The  truth  is,  that  Mr.  Lowe  here  attacks  nothing  except  the  co- 
existence of  the  florin  and  half-crown.  We  are  endeavouring  to 
abolish  .the  half-crown.  Let  Mr.  Lowe  join  us ;  and  he  will,  if  we 
succeed,  be  relieved  from  the  pressure  on  his  pocket  which  must 
arise  from,  having  the  tarn  of  the  market  always  against  him. 

"  From  a  florin  they  get  to  2  Note  the  sophism  of  expressing 

2-5ths  of  a  penny,  but  who  ever  our  coin  in  terms  of  the  penny, 
bought  anything,  who  ever  reck-  which  we  abandon,  instead  of  the 
oned  or  wished  to  reckon  in  such  florin,  which  we  retain.  Re- 
a  coin  as  that  ?  "  (Hear,  hear.)  member  that  this  2  2-5ths  is  the 

hundredth    part   of    the    pound, 

which  is  called,  as  yet,  a  cent.  Nobody  buys  anything  at  a  cent, 
because  the  cent  is  not  yet  introduced.  Nobody  reckons  in  cents  for 
the  same  reason.  Everybody  wishes  to  reckon  in  cents,  who  wishes 
to  combine  the  advantage  of  decimal  reckoning  with  the  preservation 
of  the  pound  as  the  highest  unit  of  account ;  amongst  others,  a  ma- 
jority of  the  House  of  Commons,  the  Bank  of  England,  the  majority 
of  London  bankers,  the  Chambers  of  Commerce  in  various  places,  &c. 
&c.  &c. 

"  Such  a  coin  could  never  come  Does  2^d.  never  pass  from  hand 

into  general  circulation,  because  to  hand  ?  And  is  2-|d.  so  pre- 
it  represents  nothing  which  cor-  cisely  the  modulus  of  popular 
responds  with  any  of  the  wants  wants,  that  an  alteration  of  4  per 
of  the  people."  cent,  would  make  it  useless  ?  @f 

all  the  values  which  2^d.  mea- 
sures, from  three  pounds  of  potatoes  down  to  certain  arguments  used 
in  the  House  of  Commons,  there  is  not  one  for  which  a  cent  would  not 
do  just  as  well.  Mr.  Lowe  has  fallen  into  the  misconception  of  the 
person  who  admired  the  dispensation  of  Providence  by  which  large 
rivers  are  made  to  run  through  cities  so  great  and  towns  so  many.  If 
the  cent  were  to  be  introduced  to-morrow,  straightway  the  buns  and 
cakes,  the  soda-water  bottles,  the  short  omnibus  fares,  the  bunches  of 
radishes,  &c.  &c.  &c.,  would  adapt  themselves  to  the  coin. 


MR.  LOWE   ON   DECIMAL    COINAGE. 


365 


"  If  the  proposed  system  were 
adopted,  they  would  all  be  com- 
pelled to  live  in  decimals  for 
ever  ;  if  a  man  dined  at  a  public- 
house  he  would  have  to  pay  for 
his  dinner  in  decimal  fractions. 
(Hear,  hear.)  He  objected  to 
that,  for  he  thought  that  a  man 
ought  to  be  able  to  pay  for  his 
dinner  in  integers."  (Hear,  hear, 
and  a  laugh.) 


The  confusion  of  ideas  here 
exhibited  is  most  instructive. 
The  speaker  is  under  the  im- 
pression that  we  are  introducing 
fractions:  the  truth  is,  that  we 
only  want  to  abandon  the  more 
difficult  fractions  which  we  have 
got,  and  to  introduce  easier  frac- 
tions. Does  he  deny  this  ?  Let 
us  trace  his  denial  to  its  legiti- 
mate consequences.  A  man  ought 


to  pay  for  his  dinner  in  integers. 

Now,  if  Mr.  Lowe  insists  on  it  that  our  integer  is  the  pound,  he  is 
bound  to  admit  that  the  present  integer  is  the  pound,  of  which  a 
shilling,  &c.,  are  fractions.  The  next  time  he  has  a  chop  and  a  pint 
of  stout  in  the  city,  the  waiter  should  say — "  A  pound,  sir,  to  you,"  and 
should  add,  "  Please  to  remember  the  waiter  in  integers."  Mr.  Lowe 
fancies  that  when  he  pays  one  and  sixpence,  he  pays  in  integers,  and 
so  he  does,  if  his  integer  be  a  penny  or  a  sixpence.  Let  him  bring  his 
mind  to  contemplate  a  mil  as  the  integer,  the  lowest  integer,  and  the 
seven  cents  five  mils  which  he  would  pay  under  the  new  system  would 
be  payment  in  integers  also.  But,  as  it  happens  with  some  others,  he 
looks  up  the  present  system,  with  Cocker  and  Walkingame,  and  always 
looks  down  the  proposed  system.  The  word  decimal  is  obstinately 
associated  with  fractions,  for  which  there  is  no  need.  Hence  it  be- 
comes so  much  of  a  bugbear,  that,  to  parody  the  lines  of  Pope,  which 
probably  suggested  one  of  Mr.  Lowe's  phrases — 

Dinner  he  finds  too  painful  an  endeavour, 
Condemned  to  pay  in  decimals  for  ever, 


"The  present  system,  however, 
had  not  yet  been  changed  into 
decimal  system.  That  change 
might  appear  very  easy  to  accom- 
plished mathematicians  and  men 
of  science,  but  it  was  one  which 
it  would  be  very  difficult  to  carry 
out.  (Hear,  hear).  What  would 
haye  to  be  done  ?  Every  sum 
would  have  to  be  reduced  into  a 
vulgar  fraction  of  a  pound,  and 
then  divided  by  the  decimal  of  a 
pound — a  pleasant  sum  for  an 
old  applewoman  to  work  out !  " 
(Hear,  hear,  and  laughter.) 


A  pleasant  sum  even  for 
an  accomplished  mathematician. 
What  does  divided  by  the 
decimal  of  a  pound  mean  ?  Per- 
haps it  means  reduced  to  the 
decimal  of  a  pound  !  Mr.  Lowe 
supposes,  as  many  others  do, 
that,  after  the  change,  all  calcu- 
lations will  be  proposed  in  old 
money,  and  then  converted  into 
new.  He  cannot  hit  the  idea 
that  the  new  coins  will  take  the 
place  of  the  old.  This  lack  of 
apprehension  will  presently  ap- 
pear further. 


"  It  would  not  be  an  agreeable  Let  the   members   be   assured 


366  A  BUDGET  OF  PAEADOXES. 

tisk,  even  for  some  members  of  that  nine  half-pence  will  be,  for 
that  House,  to  reduce  4^d.,  or  every  practical  purpose,  18  mils, 
nine  half-pence,  to  mils."  (Hear,  Bat  now  to  the  fact  asserted, 
hear.)  Davies  Gilbert  used  to  maintain 

that  during  the  long  period  he  sat  in  the  House,  he  never  knew  more 
than  three  men  in  it,  at  one  time,  who  had  a  tolerable  notion  of 
fractions.  [I  heard  him  give  the  names  of  three  atj  the  time  when  he 
spoke :  they  were  Warburton,  Pollock,  and  Hume.  He  himself  was 
then  out  of  Parliament.]  Joseph  Hume  affirmed  that  he  had  never 
met  with  more  than  ten  members  who  were  arithmeticians.  But  both 
these  gentlemen  had  a  high  standard.  Mr.  Lowe  has  given  a  much 
more  damaging  opinion.  He  evidently  means  that  the  general  run  of 
members  could  not  do  his  question.  It  is  done  as  follows  :  Since 
farthings  gain  on  mils,  at  the  rate  of  a  whole  mil  in  24  farthings  (24 
farthings  being  25  mils),  it  is  clear  that  18  farthings  being  three- 
quarters  of  24  farthings,  will  gain  three-quarters  of  a  mil  ;  that  is,  18 
farthings  are  eighteen  mils  and  three-quarters  of  a  mil.  Any  number 
of  farthings  is  as  many  mils  and  as  many  twenty-fourths  of  a  mil. 
To  a  certain  extent,  we  feel  able  to  protest  against  the  manner  in 
which  Kidderminster  has  treated  the  other  constituencies.  We  do 
not  hold  it  impossible  to  give  the  Members  of  the  House  in  general  a 
sufficient  knowledge  of  the  meaning  and  consequences  of  the  decimal 
succession  of  units,  tens,  hundreds,  thousands,  &c.  ;  and  we  believe 
that  there  are  in  the  House  itself  competent  men,  in  number  enough 
to  teach  all  the  rest.  All  that  is  wanted  is  the  power  of  starting  from 
the  known  to  arrive  at  the  unknown.  Now  there  is  one  kind  of 
decimals  with  which  every  member  is  acquainted — the  Ohiltern 
Hundreds.  If  public  opinion  would  enable  the  competent  minority  to 
starb  from  this  in  their  teaching,  not  as  a  basis,  but  as  an  alternative, 
in  three  weeks  the  fundamentals  would  be  acquired,  and  members  in 
general  would  be  as  fit  to  turn  4^d.  into  mils,  as  any  boys  on  the 
lower  forms  of  a  commercial  school. 

For  a  long  period  of  years,  allusion  to  the  general  ignorance  of 
arithmetic,  has  been  a  standing  mode  of  argument,  and  has  always 
been  well  received :  whenever  one  member  describes  others  as  know- 
nothings,  those  others  cry  Hear  to  the  country  in  a  transport  of  de- 
light. In  the  meanwhile  the  country  is  gradually  arriving  at  the 
conclusion  that  a  true  joke  is  no  joke. 

"The  main  objection  was,  if  Fine  words,  wrongly  used.  The 

they  went  below  6cL,  that  the  new  new  coins  are  commensurable 
scale  of  coins  would  not  be  com-  with,  and  in  a  finite  ratio  to,  the 
mensurate  in  any  finite  ratio  with  old  ones.  The  farthing  is  to  the 
anything  in  this  new  currency  of  mil  as  25  to  24.  The  speaker  has 
mils."  something  here  in  the  bud,  which 

we  shall  presently  meet  with  in 
the  flower  ;  and  fallacies  are  more 
easily  nipped  in  flower  than  in  bud. 


MR.  LOWE   ON  DECIMAL  COINAGE. 


367 


"  No  less'than  five  of  our  present 
coins  must  be   called  in,  or  else 
—  which      would     be     worse — 
new    values  must  be   given   to 
them." 

"  If  a  poor  man  put  a  penny  in 
his  pocket,  it  would  come  out  a 
coin  of  different  value,  which  he 
would  not  understand.  Suppose 
he  owed  another  man  a  penny, 
how  was  he  to  pay  him?  Was 
he  to  pay  him  in  mils  ?  Four 
mils  would  be  too  little,  and  five 
mils  would  be  too  much.  The 
hon.  gentlemen  said  there  would 
be  only  a  mil  between  them. 
That  was  exactly  it.  He  be- 
lieved there  would  be  a  '  mill '  be- 
tween them."  (Much  laughter.) 


This  dreadful  change  of  value 
consists  in  sixpence  farthing 
going  to  the  half-shilling  instead 
of  sixpence.  '-  Whether  the  new 
farthings  be  called  mils  or  not  is 
of  no  consequence. 

Mr.  Lowe,  who  cannot  pass  a 
half-crown  for  more  than  a  florin, 
or  get  in  a  florin  at  less  than 
half-a-crown,  has  such  a  high 
faith  in  the  sterner  stuff  of  his 
fellow  countrymen,  that  he  be- 
lieves any  two  of  them  would  go 
to  fisty  cuffs  for  the  25th  part  of 
a  farthing.  He  reasons  thus  : — 
He  has  often  heard  in  the  streets, 
"I'd  fight  you  for  the  fiftieth 
part  of  a  farden:"  and  having 
(that  is,  for  a  Member)  a  notion 
both  of  fractions  and  logic,  he 


infers    that     those    who     would 

fight  for  the  50th  of  a  farthing  would,  a  fortiori,  fight  for  a  25th.  His 
mistake  arises  from  his  not  knowing  that  when  a  person  offers  to  fight 
another  for  ^^d.,  he  really  means  to  fight  for  love ;  and  that  the  stake 
is  merely  a  matter  of  form,  a  feigned  issue,  a  pro  forma  report  of  pro- 
gress. Do  the  Members  of  the  House  think  they  have  all  the  forms  to 
themselves  ? 


"  What  would  be  the  present 
expression  for  fourpence  ?  Why, 
0'166  (a  laugh)  ;  for  threepence  ? 
•0125;  for  a  penny?  '004166, 
and  so  on  ad  infinitum  (a  laugh) ; 
for  a  half-penny?  -002083  ad 
infinitum.  (A  laugh).  What 
would  be  the  present  expression 
for  a  farthing  ?  Why,  '0010416 
ad  infinitum.  (A  laugh).  And 
this  was  the  system  which  was  to 
cause  such  a  saving  iri  figures, 
and  these  were  the  quantities 
into  which  the  poor  would  have 
to  reduce  the  current  coin  of 
the  realm.  (Cheers).  With  every 
respect  for  decimal  fractions,  of 
which  he  boasted  no  profound 
knowledge,  he  doubted  whether 
the  poor  were  equal  to  mental 


We  should  hardly  believe  all 
this  to  be  uttered  in  earnest,  if 
we  had  not  known  that  several 
persons  who  have  not  Mr.  Lowe's 
humour,  nevertheless  have  his 
impressions  on  this  point.  It 
must,  therefore,  be  answered : 
but  how  is  this  to  be  done 
seriously  ? 


368 


A  BUDGET   OF  PAKADOXES. 


arithmetic  of  this  kind,  (hear, 
hear)  and  he  hoped  the  adoption 
of  the  system  would  be  deferred 
until  there  were  some  proof  that 
they  would  be  able  to  understand 
it;  for,  after  all,  this  was  the 
question  of  the  poor,  and  the 
whole  weight  of  the  change  would 
fall  upon  them.  Let  the  rich  by 
all  means  have  permission  to  per- 
plex themselves  by  any  division 
of  a  pound  they  pleased  ;  but  do 
not  let  them,  by  any  experiment 
like  this,  impose  difficulties  upon 
the  poor,  and  compel  men  to 
carry  ready-reckoners  in  their 
pocket  to  give  them  all  these 
fractional  quantities."  (Hear, 
hear.) 


Dialogue  between  a  member  of 
Parliament  and  an  orange-boy, 
three  days  after  the  introduction  of 
the  complete  decimal  system.  The 
member,  going  down  to  the  House, 
wants  oranges  to  sustain  his  voice 
in  a  two  hours'  speech  on  moving 
that  100,OOOZ.  be  placed  at  the 
disposal  of  Her  Majesty,  to  supply 
the  poor  with  ready-reckoners. 

Boy.  Fine  oranges !  two  a 
penny  !  two  a  penny ! 

Member.  Here,  boy,  two ! 
Now,  how  am  I  to  pay  you  ? 

Soy.  Give  you  change,  your 
honour. 

Member.  Ah !  but  how  ? 
Where's  your  ready -reckoner  ? 

Boy.  I  sells  a  better  sort  nor 
them.  Mine's  real  Cheyny. 

Member.  But  you  see  a  far- 
thing is  now  '001  4166666  ad 
infinitum,,  and  if  we  multiply 

this  by  4 

Boy.  Hold  hard,  Guv'ner;  I 
sees  what  you're  arter.  Now, 
what' 11  you  stand  if  I  puts  you 
up  to  it  ?  which  Bill  Smith 
he  put  me  up  in  two  minutes, 
cause  he  goes  to  the  Ragged 
School. 

Member.     You  don't  mean  that  you  do  without  a  book  ! 
Boy.     Book  be  blowed.     Come  now,  old  un,  here's  summut  for  both 
on  us.     I  got  a  florin,  you  gives  me  half-a-crown  for  it,  and  I  larns 
you  the  new  money,  gives  you  your  oranges,  and  calls  you  a  brick 
into  the  bargain. 

Member  (to  himself).  Never  had  such  a  chance  of  getting  off  half-a- 
crown  for  value  since  that" fellow  Bowring  carried  his  crochet. 

(Aloud).     Well,  boy,  its  a  bargain.     Now  ! 

Boy.  Why,  look  'e  here,  my  trump,  its  a  farden  more  to  the  tizzy—- 
that's what  it  is. 

Member.     What's  that  ? 

Boy.  Why,  you  knows  a  sixpence  when  you  sees  it.  (Aside). 
Blest  if  I  think  he  does  !  Well,  its  six  browns  and  a  farden  now.  A 
lady  buys  two  oranges,  and  forks  out  a  sixpence  ;  well,  in  coorse,  I 


DECIMAL  COINAGE.  369 

hands  over  fippence  farden  astead  of  fippence.  I  always  gives  a  farden 
more  change,  and  takes  according. 

Member  (in  utter  surprise,  lets  his  oranges  tumble  into  the  gutter). 
Never  mind  !  They  won't  be  wanted  now.  (Walks  off  one  way.  Boy 
makes  a  pass  of  naso-digital  mesmerism,  and  walks  off  the  other  way). 

To  the  poor,  who  keep  no  books,  the  whole  secret  is  '  Sixpence 
farthing  to  the  half  shilling,  twelve  pence  half-penny  to  the  shil- 
ling.' The  new  twopence  halfpenny,  or  cent,  will  be  at  once  five  to  the 
shilling. 

In  conclusion,  we  remark  that  three  very  common  misconceptions 
run  through  the  hon.  Member's  argument ;  and,  combined  in  different 
proportions,  give  variety  to  his  patterns. 

First,  he  will  have  it  that  we  design  to  bring  the  uneducated  into 
contact  with  decimal  fractions.  If  it  be  so,  it  will  only  be  as  M. 
Jourdain  was  brought  into  contact  with  prose.  In  fact,  Quoi  !  ^uand 
je  dis,  Nicole,  apportez-moi  mes  pantoufles,  c'est  de  la  prose  ?  may  be 
rendered — "  What !  do  you  mean  that  ten  to  the  florin  is  a  cent  a  piece 
must  be  called  decimal  reckoning  ? "  If  we  had  to  comfort  a  poor 
man,  horror-struck  by  the  threat  of  decimals,  we  should  tell  him  what 
manner  of  fractions  had  been  inflicted  upon  him  hitherto ;  nothing 
less  awful  than  quarto-duodecimo-vicesimals,  we  should  assure  him. 

Secondly,  he  assumes  that  the  penny,  such  as  it  now  is,  will  remain, 
as  a  coin  of  estimation,  after  it  has  cease.l  to  be  a  coin  of  exchange  ; 
and  that  the  mass  of  the  people  will  continue  to  think  of  prices  in  old 
pence,  and  to  calculate  them  in  new  ones,  or. else  in  new  mils.  No 
answer  is  required  to  this,  beyond  the  mere  statement  of  the  nature  of 
the  assumption  and  denial. 

Thirdly,  he  attributes  to  the  uneducated  community  a  want  of  per- 
ception and  of  operative  power  which  really  does  not  belong  to  them. 
The  evidence  offered  to  the  Committee  of  the  House  shows  that  no 
fear  is  entertained  on  this  point  by  those  who  come  most  in  contact 
with  farthing  purchasers.  And  this  would  seem  to  be  a  rule,  — that  is, 
fear  of  the  intelligence  of  the  lower  orders  in  the  minds  of  those  who 
are  not  in  daily  communication  with  them,  no  fear  at  all  in  the  minds 
of  those  who  are. 

A  remarkable  instance  of  this  distinction  happened  five-and-twenty 
years  ago.  The  Admiralty  requested  the  Astronomical  Society  to 
report  on  the  alterations  which  should  be  made  in  the  Nautical 
Almanac,  the  seaman's  guide-book  over  the  ocean.  The  greatest 
alteration  proposed  was  the  description  of  celestial  phenomena  in  mean 
(or  clock  time),  instead  of  apparent  (or  sundial)  time,  till  then  always 
employed.  This  change  would  require  that  in  a  great  many  operations 
the  seaman  should  let  alone  what  he  formerly  altered  by  addition  or 
subtraction,  and  alter  by  addition  or  subtraction  what  he  formerly  let 
alone ;  provided  always  that  what  he  formerly  altered  by  addition  he 
should,  when  he  altered  at  all,  alter  by  subtraction,  and  vice  versa. 
This  was  a  tolerably  difficult  change  for  uneducated  skippers,  working 

B  B 


370  A   BUDGET   OF   PARADOXES. 

by  rules  they  had  only  learned  by  rote.  The  Astronomical  Society 
appointed  a  Committee  of  forty,  of  whom  nine  were  naval  officers  or 
merchant  seamen  [I  was  on  this  Committee].  Some  men  of  science 
were  much  afraid  of  the  change.  They  could  not  trust  an  ignorant 
skipper  or  mate  to  make  those  alterations  in  their  routine,  on  the 
correctness  of  which  the  ship  might  decend.  Had  the  Committee 
consisted  of  men  of  science  only,  the  change  might  never  have  been 
ventured  on.  But  the  naval  men  laughed,  and  said  there  was  nothing 
to  fear  ;  and  on  their  authority  the  alteration  was  made.  The  upshot 
was,  that,  after  the  new  almanacs  appeared,  not  a  word  of  complaint 
was  ever  heard  on  the  matter.  Had  the  House  of  Commons  had  to 
decide  this  question,  with  Mr.  Lowe  to  quote  the  description  given  by 
Basil  Hall  (who,  by  the  way,  was  one  of  the  Committee)  of  an  obser- 
vation on  which  the  safety  of  the  ship  depended,  worked  out  by  the 
light  of  a  lantern  in  a  gale  of  wind  off  a  lee  shore,  this  simple  and 
useful  change  might  at  this  moment  have  been  in  the  hands  of  i(s 
tenth  Government  Commission.' 

[Aug.  14,  1866.  The  Committee  was  appointed  in  the  spring  of 
1830  :  it  consisted  of  forty  members.  Death,  of  course,  has  been  busy  : 
there  are  now  left  Lord  Shaffcesbury,  Mr.  Babbage,  Sir  John  Herschel, 
Sir  Thomas  Maclear  (Astronomer  Royal  at  the  Cape  of  Good  Hope), 
Dr.  Robinson  (of  Armagh),  Sir  James  South,  Lord  Wrottesley,  and 
myself]. 

Project  of  a  new  system  of  arithmetic,  weight,  measure,  and  coins, 
proposed  to  be  called  the  tonal  system,  with  sixteen  to  the  base. 
By  J.  W.  Mystrom.  Philadelphia,  1862,  8vo. 

That  is  to  say,  sixteen  is  to  take  the  place  of  ten,  and  to  be 
written  10.  The  whole  language  is  to  be  changed  ;  every  man  of 
us  is  to  be  sixteen-stringed  Jack  and  every  woman  sixteen- 
stringed  Jill.  Our  old  one.,  two,  three,  up  to  sixteen,  are  to  be 
(Noll  going  for  nothing,  which  will  please  those  who  dislike  the 
memory  of  Old  Noll}  replaced  by  An,  De,  Ti,  Go,  Su,  By,  Ka,  Me, 
Ni,  Ko,  Hu,  Vy,  La,  Po,  Fy,  Ton ;  and  then  Ton-an,  Ton-de,  &c. 
for  17,  18,  &c.  The  number  which  in  the  system  has  the  symbol 

28(13)5(11)7(14)0(15) 

(using  our  present  compounds  instead  of  new  types)  is  to  be  pro- 
nounced 

Detam-memill-lasan-suton-hubong-ramill-posanfy. 
The  year  is  to  have  sixteen  months,  and  here  they  are  : — 

Anuary,  Debrian,  Timander,  Gostus, 
•$  Suvenary,  By  Han,  Ratamber,  Mesudius, 

Nictoary,  Kolumbian,  Husamber,  Vyctorius, 
Lamboary,  Polian,  Fy  lander,  Tonborius. 


THE   "TONAL"   SYSTEM.  371 

Surely  An-month,  De-month,  &c.  would  do  as  well.  Probably 
the  wants  of  poetry  were  considered.  But  what  are  we  ta  do  with 
our  old  poets  ?  For  example — 

It  was  a  night  of  lovely  June, 

High  rose  in  cloudless  blue  the  moon. 

Let  us  translate — 

It  was  a  night  of  lovely  Nictoary, 

High  rose  in  cloudless  blue  the  (what,  in  the  name  of 
all  that  is  absurd  ?). 

And  again,  Fylander  thrown  into  our  December !  What  is  to 
become  of  those  lines  of  Praed,  which  I  remember  coming  out 
when  I  was  at  Cambridge, — 

Oh !  now's  the  time  of  all  the  year  for  flowers  and  fun,  the  May-days  ; 
To  trim  your  whiskers,  curl  your  hair,  and  sinivate  the  ladies. 

If  I  were  asked  which  I  preferred,  this  system  or  that  of  Baron 
Ferrari  already  mentioned,  proceeding  by  twelves,  I  should  reply, 
with  Candide,  when  he  had  the  option  given  of  running  the 
gauntlet  or  being  shot :  Les  volontes  sont  libres,  et  je  ne  veux  ni 
1'un  ni  1'autre.  We  can  imagine  a  speculator  providing  such  a 
system  for  Utopia  as  it  would  be  in  the  mind  of  a  Laputan :  but 
to  explain  how  an  engineer  who  has  surveyed  mankind  from 
Philadelphia  to  Kostof  on  the  Don  should  for  a  moment  entertain 
the  idea  of  such  a  system  being  actually  adopted,  would  beat  a 
jury  of  solar-system-makers,  though  they  were  shut  up  from  the 
beginning  of  Anuary  to  the  end  of  Tonborius.  When  I  see  such 
a  scheme  as  this  imagined  to  be  practicable,  I  admire  the  wisdom 
of  Providence  in  providing  the  quadrature  of  the  circle,  &c.,  to 
open  a  harmless  sphere  of  action  to  the  possessors  of  the  kind  of 
ingenuity  which  it  displays.  Those  who  cultivate  mathematics 
have  a  right  to  speak  strongly  on  such  efforts  of  arithmetic  as 
this  :  for,  to  my  knowledge,  persons  who  have  no  knowledge  are 
frequently  disposed  to  imagine  that  their  makers  are  true 
brothers  of  the  craft,  .a  little  more  intelligible  than  the  rest. 

Vis  inertiae  victa,  or  Fallacies  affecting  science.    By  James  Reddie. 
London,  1862,  8vo. 

An  attack  on  the  Newtonian  mechanics ;  revolution  by  gravi- 
tation demonstrably  impossible ;  much  to  be  said  for  the  earth 
being  the  immovable  centre.  A  good  analysis  of  contents  at  the 
beginning,  a  thing  seldom  found.  The  author  has  followed  up 

B    H    '.>. 


372  A   BUDGET   OF  PARADOXES. 

his  attack  in  a  paper  submitted  to  the  British  Association,  but 
which  it  appears  the  Association  declined  to  consider.  It  is 
entitled — 

Victoria   Toto   Coelo ;    or,   Modern   Astronomy   recast.      London, 
18G3,  8vo. 

At  the  end  is  a  criticism  of  Sir  G.  Lewis's  '  History  of  Ancient 
Astronomy.' 

On  the  definition  and  nature  of  the  Science  of  Political  Economy. 
By  H.  Dunning  Macleod,  Esq.     Cambridge,  1862,  8vo. 

A  paper  read — but,  according  to  the  report,  not  understood — at 
the  British  Association.  There  is  a  notion  that  political  economy 
is  entirely  mathematical;  and  its  negative  quantity  is  strongly 
recommended  for  study :  it  contains  '  the  whole  of  the  Funds, 

Credit,  32  parts  out  of  33  of  the  value  of  Land '     The 

mathematics  are  described  as  consisting  of- — first,  number,  or 
Arithmetic  ;  secondly,  the  theory  of  dependent  quantities,  sub- 
divided into  dependence  by  cause  and  effect,  and  dependence  by 
simultaneous  variations ;  thirdly,  '  independent  quantities  or 
unconnected  events,  which  is  the  theory  of  probabilities.'  I  am 
not  ashamed,  having  the  British  Association  as  a  co-non-intel- 
ligent,  to  say  I  do  not  understand  this :  there  is  a  paradox  in  it, 
and  the  author  should  give  further  explanation,  especially  of  his 
negative  quantity.  Mr.  Macleod  has  gained  praise  from  great 
names  for  his  political  economy ;  but  this,  1  suspect,  must  have 
been  for  other  parts  of  his  system. 

On  the  principles  and  practice  of  just  Intonation,  with  a  view  to 
the  abolition  of  temperament  .  .  .  By  General  Perronet  Thomp- 
son. Sixth  Edition.  London,  1862,  8vo. 

Here  is  General  Thompson  again,  with  another  paradox :  but 
always  master  of  the  subject,  always  well  up  in  what  his  prede- 
cessors have  done,  and  always  aiming  at  a  useful  end.  He  desires 
to  abolish  temperament  by  additional  keys,  and  has  constructed 
an  enharmonic  organ  with  forty  sounds  in  the  octave.  If  this  can 
be  introduced,  I,  for  one,  shall  delight  to  hear  it :  but  there  are 
very  great  difficulties  in  the  way,  greater  than  stood  even  in  the 
way  of  the  repeal  of  the  bread-tax. 

In  a  paper  on  the  beats  of  organ-pipes  and  on  temperament 
published  some  years  ago,  I  said  that  equal  temperament  ap- 
peared to  me  insipid,  and  not  so  agreeable  as  the  effect  of  the 


DUAL   ARITHMETIC.  373 

instrument  when  in  progress  towards  being  what  is  called  out  of 
tune,  before  it  becomes  offensively  wrong.  There  is  throughout 
that  period  unequal  temperament,  determined  by  accident. 
General  Thompson,  taking  me  one  way,  says  I  have  launched  a 
declaration  which  is  likely  to  make  an  epoch  in  musical  practice; 
a  public  musical  critic,  taking  me  another  way,  quizzes  me  for 
preferring  music  out  of  tune.  I  do  not  think  I  deserve  either 
one  remark  or  the  other.  My  opponent  critic,  I  suspect,  takes 
equally  tempered  and  in  tune  to  be  phrases  of  one  meaning. 
But  by  equal  temperament  is  meant  equal  distribution  among  all 
the  keys  of  the  error  which  an  instrument  must  have,  which,  with 
twelve  sounds  only  in  the  octave,  professes  to  be  fit  for  all  the 
keys.  I  am  reminded  of  the  equal  temperament  which  was  once 
applied  to  the  postmen's  jackets.  The  coats  were  all  made  for 
the  average  man:  the  consequence  was  that  all  the  tall  men  had 
their  tails  too  short ;  all  the  short  men  had  them  too  long. 
Some  one  innocently  asked  why  the  tall  men  did  not  change  coats 
with  the  short  ones. 

A  diagram  illustrating  a  discovery  in  the  relation  of  circles  to 
right-lined  geometrical  figures.     London,  1863,  12mo. 

The  circle  is  divided  into  equal  sectors,  which  are  joined  head 
and  tail :  but  a  property  is  supposed  which  is  not  true. 

An  attempt  to  assign  the  square  roots  of  negative  powers  ;  or 
what  is  A/  -  1  ?     By  F.  H.  Laing.     London,  1863,  8vo. 

If  I  understand  the  author,  —  a  and  +aare  the  square  roots 
of  —  a2,  as  proved  by  multiplying  them  together.  The  author 
seems  quite  unaware  of  what  has  been  done  in  the  last  fifty 
years. 

Dual    Arithmetic.      A    new   art.     By   Oliver   Byrne.      London, 
1863,  8vo. 

The  plan  is  to  throw  numbers  into  the  form  a(l'l)6  (TOl)" 

(l'001)d and  to  operate  with  this  form.  This  is  an  ingenious 

and  elaborate  speculation  ;  and  I  have  no  doubt  the  author  has 
practised  his  method  until  he  could  surprise  any  one  else  by  his 
use  of  it.  But  I  doubt  if  he  will  persuade  others  to  use  it.  As 
asked  of  Wilkins's  universal  language,  Where  is  the  second  man 
to  come  from  ? 

An  effective  predecessor  in  the  same  line  of  invention  was  the 
late  Mr.  Thomas  Weddle,  in  his  '  New,  simple,  and  general  method 


374  A   BUDGET   OF   PARADOXES. 

of  solving  numeric  equations  of  all  orders,'  4to,  1842.  The 
Royal  Society,  to  which  this  paper  was  offered,  declined  to  print 
it :  they  ought  to  have  printed  an  organised  method,  which,  with- 
out subsidiary  tables,  showed  them,  in  six  quarto  pages,  the 
solution  (x*=  8-367975431)  of  the  equation 

1379'664a;C22  +  2686034  x  1043V53- 17290224  x  1051saj60+ 2524156 

x  10"4  =  0. 

The  method  proceeds  by  successive  factors  of  the  form,  a  being 

the  first  approximation,  a  x  1*6  x  1'Oc  x  1'OOcZ In 

my  copy  I  find  a  few  corrections  made  by  me  at  the  time  in  Mr. 
Weddle's  announcement.  'It  was  read  before  that  learned  body 
[the  R.  S.]  and  they  were  pleased  [but]  to  transmit  their  thanks 
to  the  author.  The  en[dis]couragement  which  he  received  induces 
[obliges]  him  to  lay  the  result  of  his  enquiries  in  this  important 
branch  of  mathematics  before  the  public  [,  at  his  own  expense ; 
he  being  an  usher  in  a  school  at  Newcastle].  Which  is  most 
satirical,  Mr.  Weddle  or  myself?  The  Society,  in  the  account 
which  it  gave  of  this  paper,  described  it  as  a  '  new  and  remark- 
ably simple  method '  possessing  '  several  important  advantages.' 
Mr.  Rutherford's  extended  value  of  TT  was  read  at  the  very  next 
meeting,  and  was  printed  in  the  Transactions ;  and  very 
properly :  Mr.  Weddle's  paper  was  excluded,  and  very  very 
improperly. 

I  think  it  may  be  admitted  that  the  indisposition  to  look  at 
and  encourage  improvements  of  calculation  which  once  marked 
the  Royal  Society  is  no  longer  in  existence.  But  not  without 
severe  lessons.  They  had  the  luck  to  accept  Homer's  now  cele- 
brated paper,  containing  the  method  which  is  far  on  the  way  to 
become  universal :  but  they  refused  the  paper  in  which  Homer 
developed  his  views  of  this  and  other  subjects :  it  was  printed  by 
T.  S.  Davies  after  Horner's  death.  I  make  myself  responsible  for 
the  statement  that  the  Society  could  not  reject  this  paper,  yet 
felt  unwilling  to  print  it,  and  suggested  that  it  should  be  with- 
drawn ;  which  was  done. 

But  the  severest  lesson  was  the  loss  of  Barrett's  Method,  now 
the  universal  instrument  of  the  actuary  in  his  highest  calculations. 
It  was  presented  to  the  Royal  Society,  and  refused  admission  into 
the  Transactions  :  Francis  Baily  printed  it.  The  Society  is  now 
better  informed  :  '  live  and  learn,'  meaning  '  must  live,  so  better 
learn,'  ought  to  be  the  especial  motto  of  a  corporation,  and  is 
generally  acted  on,  more  or  less. 

Horner's  method  begins  to  be  introduced  at  Cambridge  :  it  was 


HORNER'S   METHOD.  375 

published  in  1820.  I  remember  that  when  I  first  went  to 
Cambridge  (in  1823)  I  heard  my  tutor  say,  in  conversation,  there 
is  no  doubt  that  the  true  method  of  solving  equations  is  the  one 
which  was  published  a  few  years  ago  in  the  Philosophical  Trans- 
actions. I  wondered  it  was  not  taught,  but  presumed  that  it 
belonged  to  the  higher  mathematics.  This  Horner  himself  had 
in  his  head :  and  in  a  sense  it  is  true ;  for  all  lower  branches 
belong  to  the  higher:  but  he  would  have  stared  to  have  been 
told  that  lie,  Horner,  was  without  a  European  predecessor,  and, 
in  the  distinctive  part  of  his  discovery  was  heir-at-law  to  the 
nameless  Brahmin — Tartar — Antenoachian — what  you  please — 
who  concocted  the  extraction  of  the.  square  root. 

It  was  somewhat  more  than  twenty  years  after  I  had  thus  heard 
a  Cambridge  tutor  show  sense  of  the  true  place  of  Homer's 
method,  that  a  pupil  of  mine  who  had  passed  on  to  Cambridge 
was  desired  by  his  college  tutor  to  solve  a  certain  cubic  equation 
—one  of  an  integer  root  of  two  figures.  In  a  minute  the  work 
and  answer  were  presented,  by  Horner's  method.  '  How  ! '  said  the 
tutor,  '  this  can't  be,  you  know.'  '  There  is  the  answer,  Sir ! '  said 
my  pupil,  greatly  amused,  for  my  pupils  learnt,  not  only  Horner's 
method,  but  the  estimation  it  held  at  Cambridge.  *  Yes ! '  said  the 
tutor,  c  there  is  the  answer  certainly ;  but  it  stands  to  reason  that 
a  cubic  equation  cannot  be  solved  in  this  space.'  He  then  sat 
down,  went  through  a  process  about  ten  times  as  long,  and  then 
said  with  triumph :  '  There  !  that  is  the  way  to  solve  a  cubic 
equation ! ' 

I  think  the  tutor  in  this  <^,se  was  never  matched,  except  by  the 
country  organist.  A  master  of  the  instrument  went  into  the  organ- 
loft  during  service,  and  asked  the  organist  to  let  \\inaplay  the  con- 
gregation out ;  consent  was  given.  The  stranger,  when  the  time 
came,  began  a  voluntary  which  made  the  people  open  their  ears, 
and  wonder  who  had  got  into  the  loft :  they  kept  their  places  to 
enjoy  the  treat.  When  the  organist  saw  this,  he  pushed  the 
interloper  off  the  stool,  with  '  You'll  never  play  'em  out  this  side 
Christmas.'  He  then  began  his  own  drone,  and  the  congregation 
began  to  move  quietly. away.  '  There,'  said  he,  '  that's  the  way  to 
play  'em  out ! ' 

I  have  not  scrupled  to  bear  hard  on  my  own  University,  on  the 
Koyal  Society,  and  on  other  respectable  existences :  being  very 
much  the  friend  of  all.  I  will  now  clear  the  Royal  Society  from 
a  very  small  and  obscure  slander,  simply  because  I  know  how. 
This  dissertation  began  with  the  work  of  Mr.  Oliver  Byrne,  the 
dual  arithmetician,  &c.  This  writer  published,  in  1849,  a  method 


376  A  BUDGET   OF  PARADOXES. 

of  calculating  logarithms.  First,  a  long  list  of  instances  in  which, 
as  he  alleges,  foreign  discoverers  have  been  pillaged  by  English- 
men, or  turned  into  Englishmen  :  for  example,  O'Neill,  so  called 
by  Mr.  Byrne,  the  rectifier  of  the  semi-cubical  parabola  claimed 
by  the  Saxons  under  the  name  of  Need :  the  grandfather  of  this 
mathematician  was  conspicuous  enough  as  Neal;  he  was  Arch- 
bishop of  York.  This  list,  says  the  writer,  might  be  continued 
without  end  ;  but  he  has  mercy,  and  finishes  with  his  own  case,  as 
follows  : — '  About  twenty  years  ago,  I  discovered  this  method  of 
directly  calculating  logarithms.  I  could  generally  find  the  loga- 
rithm of  any  number  in  a  minute  or  two  without  the  use  of  books 
or  tables.  The  importance  of  the  discovery  subjected  me  to  all 
sorts  of  prying.  Some  asserted  that  I  committed  a  table  of 
logarithms  to  memory ;  others  attributed  it  to  a  peculiar  mental 
property;  and  when  Societies  and  individuals  failed  to  extract 
my  secret,  they  never  failed  to  traduce  the  inventor  and  the 
invention.  Among  the  learned  Societies,  the  Eoyal  Society  of 
London  played  a  very  base  part.  When  I  have  more  space  and 
time  at  my  disposal,  I  will  revert  to  this  subject  again.' 

Such  a  trumpery  story  as  this  remains  unnoticed  at  the  time  ; 
but  when  all  are  gone,  a  stray  copy  from  a  stall  falls  into  hands 
which,  not  knowing  what  to  make  of  it,  make  history  of  it.  It 
is  a  very  curious  distortion.  The  reader  may  take  it  on  my 
authority,  that  the  Eoyal  Society  played  no  part,  good  or  bad,  nor 
had  the  option  of  playing  a  part.  But  I  myself  pars  magna  fui : 
and  when  the  author  has  '  space  and  time '  at  his  disposal,  he 
must  not  take  all  of  them  ;  I  shall  want  a  little  of  both. 


The  mystery  of  being ;  or  are  ultimate  atoms  inhabited  worlds  ? 
By  Nicholas  Odgers.     Redruth  and  London,  1863,  8vo. 

This  book,  as  a  paradox,  beats  quadrature,  duplication,  trisec- 
tion,  philosopher's  stone,  perpetual  motion,  magic,  astrology, 
mesmerism,  clairvoyance,  spiritualism,  homoeopathy,  hydropathy, 
kinesipathy,  Essays  and  Eeviews,  and  Bishop  Colenso,  all  put 
together.  Of  all  the  suppositions  I  have  given  as  actually  argued, 
this  is  the  one  which  is  hardest  to  deny,  and  hardest  to  admit. 
Eeserving  the  question — as  beyond  human  discussion — whether 
our  particles  of  carbon,  &c.  are  clusters  of  worlds,  the  author 
produces  his  reasons  for  thinking  that  they  are  at  least  single 
worlds.  Of  course — though  not  mentioned — the  possibility  is  to 
be  added  of  the  same  thing  being  true  of  the  particles  which 
make  up  our  particles,  and  so  down,  for  ever  :  and,  on  the  other 


ARE   ATOMS  WORLDS  ?  377 

hand,  of  our  planets  and  stars  as  being  particles  in  some  larger 
universe,  and  so  up,  for  ever. 

Great  fleas  have  little  fleas  upon  their  backs  to  bite  'em, 

And  little  fleas  have  lesser  fleas,  and  so  ad  infinitum. 

And  the  great  fleas  themselves,  in  turn,  have  greater  fleas  to  go  on  ; 

While  these  again  have  greater  still,  and  greater  still,  and  so  on. 

I  have  often  had  the  notion  that  all  the  nebulae  we  see,  in- 
cluding our  own,  which  we  call  the  Milky  Way,  may  be  particles 
of  snuff  in  the  box  of  a  giant  of  a  proportionately  larger  universe. 
Of  course  the  minim  of  time — a  million  of  years  or  whatever  the 
geologists  make  it — which  our  little  affair  has  lasted,  is  but  a 
very  small  fraction  of  a  second  to  the  great  creature  in  whose 
nose  we  shall  all  be  in  a  few  tens  of  thousands  of  millions  of 
millions  of  millions  of  years. 

All  this  is  quite  possible,  and  the  probabilities  for  and  against 
are  quite  out  of  our  reach.  Perhaps  also  all  the  worlds,  both 
above  and  below  us,  are  fac-similes  of  our  own.  If  so,  away  goes 
free  will  for  good  and  all ;  unless,  indeed,  we  underpin  our 
system  with  the  hypothesis  that  all  the  fac-simile  bodies  of 
different  sizes  are  actuated  by  a  common  soul.  These  acute 
supplementary  notions  of  mine  go  far  to  get  rid  of  the  difficulty 
which  some  have  found  in  the  common  theory  that  the  soul 
inhabits  the  body :  it  has  been  started  that  there  is,  somewhere 
or  another,  a  world  of  souls  which  communicate  with  their 
bodies  by  wondrous  filaments  of  a  nature  neither  mental  nor 
material,  but  of  a  tertium  quid  fit  to  be  a  go-between  ;  as  it 
were  a  corporispiritual  copper  encased  in  a  spiritucorporeal  gutta- 
percha.  My  theory  is  that  every  soul  is  everywhere  in  posse,  as 
the  schoolmen  said,  but  not  anywhere  in  actu,  except  where  it 
finds  one  of  its  bodies.  These  a  priori  difficulties  being  thus 
removed,  the  system  of  particle-worlds  is  reduced  to  a  dry  question 
of  fact,  and  remitted  to  the  decision  of  the  microscope.  And  a 
grand  field  may  thus  be  opened,  as  optical  science  progresses ! 
For  the  worlds  are  not  fac-similes  of  ours  in  time  :  there  is  not  a 
moment  of  our  past,  and  not  a  moment  of  our  future,  but  is  the 
present  of  one  or  more  of  the  particles.  A  will  write  the  death  of 
Caesar,  and  B  the  building  of  the  Pyramids,  by  actual  observation 
of  the  processes  with  a  power  of  a  thousand  millions ;  C  will 
discover  the  commencement  of  the  Millennium,  and  D  the 
termination  of  Ersch  and  Gruber's  Lexicon,  as  mere  physical 
phenomena.  Against  this  glorious  future  there  is  a  sad  omen  : 
the  initials  of  the  forerunner  of  this  discovery  are — NO ! 


378  A   BUDGET   OF   PARADOXES. 


The  History  of  the  Supernatural  in  all  ages  and  nations,  and  in 
all  Churches,  Christian  and  Pagan  :  demonstrating  a  universal 
faith.  By  Wm.  Howitt.  London,  2  vols.  8vo.  1863. 

Mr.  Howitt  is  a  preacher  of  spiritualism.  He  cements  an 
enormous  collection  of  alleged  facts  with  a  vivid  outpouring 
of  exhortation,  and  an  unsparing  flow  of  sarcasm  against  the 
scorners  of  all  classes.  He  and  the  Eev.  J.  Smith  (ante,  1854) 
are  the  most  thoroughgoing  universalists  of  all  the  writers  I 
know  on  spiritualism.  If  either  can  insert  the  small  end  of  the 
wedge,  be  will  not  let  you  off  one  fraction  of  the  conclusion  that 
all  countries,  in  all  ages,  have  been  the  theatres  of  one  vast 
spiritual  display.  And  I  suspect  that  this  consequence  cannot  be 
avoided,  if  any  part  of  the  system  be  of  truly  spiritual  origin. 
Mr.  Howitt  treats  the  philosophers  either  as  ignorant  babies,  or 
as  conscious  spirit-fearers  :  and  seems  much  inclined  to  accuse  the 
world  at  large  of  dreading,  lest  by  the  actual  presence  of  the  other 
world  their  Christianity  should  imbibe  a  spiritual  element  which 
would  unfit  it  for  the  purposes  of  their  lives. 


From  Matter  to  Spirit.     By  C.  D.     With  a  preface  by  A.  B. 
London,  1863,  8vo. 

This  is  a  work  on  Spiritual  Manifestations.  The  author  up- 
holds the  facts  for  spiritual  phenomena  :  the  prefator  suspends  his 
opinion  as  to  the  cause,  though  he  upholds  the  facts.  The  work 
begins  systematically  with  the  lower  class  of  phenomena,  proceeds 
to  the  higher  class,  and  offers  a  theory,  suggested  by  the  facts,  of 
the  connexion  of  the  present  and  future  life.  I  agree  in  the 
main  with  A.  B.  ;  but  can,  of  course,  make  none  but  horrescent 
reference  to  his  treatment  of  the  smaller  philosopher.  This  is 
always  the  way  with  your  paradoxers  :  they  behave  towards 
orthodoxy  as  the  thresher  fish  behaves  towards  the  whale.  But 
if  true,  as  is  said,  that  the  drubbing  clears  the  great  fish  of 
parasites  which  he  could  not  otherwise  get  rid  of,  he  ought  to 
bear  no  malice.  This  preface  retorts  a  little  of  that  contempt 
which  the  'philosophical  world'  has  bestowed  with  heaped 
measure  upon  those  who  have  believed  their  senses,  and  have 
drawn  natural,  even  if  hasty,  inferences.  There  is  philosopher- 
craft  as  well  as  priestcraft,  both  from  one  source,  both  of  one 
spirit.  In  English  cities  and  towns,  the  minister  of  religion  has 
been  tamed  :  so  many  weapons  are  bared  against  him  when  he 
obtrudes  his  office  in  a  dictatory  manner  that,  as  a  rule,  there  is 


'FROM   MATTER   TO   SPIRIT.'  379 

no  more  quiet  and  modest  member  of  society  than  the  urban 
clergyman.  Domination  over  religious  belief  is  reserved  for  the 
exclusive  use  of  those  who  admit  the  right :  the  rare  exception 
to  this  mode  of  behaviour  is  laughed  at  as  a  bigot,  or  shunned  as 
a  nuisance.  But  the  overbearing  minister  of  nature,  who  snaps 
you  with  unphilosophical  as  the  clergyman  once  frightened  you 
with  infidel,  is  still  a  recognized  member  of  society,  wants  taming, 
and  will  get  it.  He  wears  the  priest's  cast-off  clothes,  dyed  to 
escape  detection  :  the  better  sort  of  philosophers  would  gladly  set 
him  to  square  the  circle. 

The  book  just  named  appeared  about  the  same  time  as  this 
Budget  began  in  the  Athenceum.  It  was  commonly  attributed, 
the  book  to  my  wife,  the  preface  to  myself.  Some  time  after, 
our  names  were  actually  announced  by  the  publisher,  who  ought 
to  know.  It  will  be  held  to  confirm  this  statement  that  I 
announce  our  having  in  our  possession  some  twenty  reviews  of 
different  lengths,  and  of  all  characters :  who  ever  collects  a 
number  of  reviews  of  a  book,  except  the  author  ? 

A  great  many  of  these  reviews  settle  the  matter  a  priori.  If 
there  had  been  spirits  in  the  matter,  they  would  have  done  this, 
and  they  would  not  have  done  that.  Jean  Meslier  said  there 
could  be  no  God  over  all,  for,  if  there  had  been  one,  He  would  have 
established  a  universal  religion.  If  J.  M.  knew  that,  J.  M.  was 
right :  but  if  J.  M.  did  not  know  that,  then  J.  M.  was  on  the 
*  high  priori  road,'  and  may  be  left  to  his  course.  The  same  to 
all  who  know  what  spirits  would  do  and  would  not  do. 

A.  B.  very  distinctly  said  that  he  knew  some  of  the  asserted 
facts,  believed  others  on  testimony,  but  did  not  pretend  to  know 
whether  they  were  caused  by  spirits,  or  had  some  unknown  and 
unimagined  origin.  This  he  said  as  clearly  as  I  could  have  said 
it  myself.  But  a  great  many  persons  cannot  understand  such  a 
frame  of  mind  :  their  own  apparatus  is  a  kind  of  spirit-level,  and 
their  conclusion  on  any  subject  is  the  little  bubble,  which  is 
always,  at  one  end  or  the  other.  Many  of  the  reviewers  declare 
that  A.  B.  is  a  secret  believer  in  the  spirit-hypothesis :  and  one 
of  them  wishes  that  he  had  '  endorsed  his  opinion  more  boldly.' 
According  to  this  reviewer,  anyone  who  writes  '  I  boldly  say  I  am 
unable  to  choose,'  contradicts  himself.  In  truth,  a  person  who 
does  say  it  has  a  good  deal  of  courage,  for  each  side  believes  that 
he  secretly  favours  the  other ;  and  both  look  upon  him  as  a 
coward.  In  spite  of  all  this,  A.  B.  boldly  repeats  that  he  feels 
assured  of  many  of  the  facts  of  spiritualism,  and  that  he  cannot 
pretend  to  affirm  or  deny  anything  about  their  cause. 


380  A   BUDGET   OF  PARADOXES. 

The  great  bulk  of  the  illogical  part  of  the  educated  community 
— whether  majority  or  minority  I  know  not ;  perhaps  six  of  one 
and  half-a-dozen  of  the  other — have  not  power  to  make  a  dis- 
tinction, cannot  be  made  to  take  a  distinction,  and  of  course, 
never  attempt  to  shake  a  distinction.  With  them  all  such  things 
are  evasions,  subterfuges,  come-offs,  loopholes,  &c.  They  would 
hang  a  man  for  horse-stealing  under  a  statute  against  sheep- 
stealing  ;  and  would  laugh  at  you  if  you  quibbled  about  the 
distinction  between  a  horse  and  a  sheep.  I  divide  the  illogical — 
I  mean  people  who  have  not  that  amount  of  natural  use  of  sound 
inference  which  is  really  not  uncommon — into  three  classes  : — 
First  class,  three  varieties :  the  Mddy,  the  Noddy,  and  the 
Noodle.  Second  class,  three  varieties :  the  Niddy-Noddy,  the 
Niddy-Noodle,  and  the  Noddy-Noodle.  Third  class,  undivided : 
the  Niddy-Noddy-Noodle.  No  person  has  a  right  to  be  angry 
with  me  for  more  than  one  of  these  subdivisions. 

The  want  of  distinction  was  illustrated  to  me,  when  a  boy, 
about  1820,  by  the  report  of  a  trial  which  I  shall  never  forget : 
boys  read  newspapers  more  keenly  than  men.  Every  now  and 
then  a  bench  of  country  magistrates  rather  astonishes  the  town 
populations,  accustomed  to  rub  their  brains  l  against  one  another. 
Such  a  story  as  the  following  would,  in  our  day,  bring  down  grave 
remarks  from  above  :  but  I  write  of  the  olden  (or  Eldon)  time, 
when  nothing  but  conviction  in  a  court  of  record  would  displace 
a  magistrate.  In  that  day  the  third-class  amalgamator  of  distinct 
things  was  often  on  the  bench  of  quarter-sessions. 

An  attorney  was  charged  with  having  been  out  at  night, 
poaching.  A  clear  alibi  was  established ;  and  perjury  had 
certainly  been  committed.  The  whole  gave  reason  to  suspect 
that  some  ill-willers  thought  the  bench  disliked  the  attorney 
so  much  that  any  conviction  was  certain  on  any  evidence.  The 
bench  did  dislike  the  attorney :  but  not  to  the  extent  of 
thinking  he  could  snare  any  partridges  in  the  fields  while  he 
was  asleep  in  bed,  except  the  dream-partridges  which  are  not 
always  protected  by  the  dream-laws.  So  the  chairman  said, 

"  Mr. ,  you  are  discharged  ;  but  you  should  consider  this 

one  of  the  most  fortunate  days  of  your  life."  The  attorney 
indignantly  remonstrated,  but  the  magistrate  was  right ;  for 

he  said,  "  Mr.  ,  you  have  frequently  been  employed  to 

defend  poachers  :  have  you  been  careful  to  impress  upon  them  the 

1  Baron  Zacli  relates  that  a  friend  of  his.  in  a  writing  intended  for  publication,  said 
Un  esprit  doit  se  frotter  centre  un  autre.  The  censors  struck  it  out.  The  Austrian 
police  have  a  keen  eye  for  consequences. 


'  FROM   MATTER   TO   SPIEIT.'  381 

enormity  of  their  practices  ?  "  It  appeared  in  a  wrangling  conver- 
sation that  the  magistrates  saw  little  moral  difference  between 
poaching  and  being  a  poacher's  professional  defender  without 
lecturing  him  on  his  wickedness:  but  they  admitted  with 
reluctance,  that  there  was  a  legal  distinction ;  and  the  brain  of 
N3  could  no  further  go.  This  is  nearly  fifty  years  ago ;  and 
Westernism  was  not  quite  extinct.  If  the  present  lords  of  the 
hills  and  the  valleys  want  to  shine,  let  them  publish  a  true 
history  of  their  own  order.  I  am  just  old  enough  to  remember 
some  of  the  last  of  the  squires  and  parsons  who  protested  against 
teaching  the  poor  to  read  and  write.  They  now  write  books  for 
the  working  classes,  give  them  lectures,  and  the  like.  There  is 
now  no  class,  as  a  class,  more  highly  educated,  broadly  educated, 
and  deeply  educated,  than  those  who  were,  in  old  times,  best 
described  as  partridge-popping  squireens.  I  have  myself,  when  a 
boy,  heard  Old  Booby  speaking  with  pride  of  Young  Booby  as 
having  too  high  a  spirit  to  be  confined  to  books :  and  J  suspected 
that  his  dislike  to  teaching  the  poor  arose  in  fact  from  a  feeling 
that  they  would,  if  taught  a  little,  pass  his  heir. 

A.  B.  recommended  the  spirit-theory  as  an  hypothesis  on 
which  to  ground  inquiry  ;  that  is,  as  the  means  of  suggestion  for 
the  direction  of  inquiry.  Every  person  who  knows  anything  of 
the  progress  of  physics  understands  what  is  meant ;  but  not  the 
reviewers  I  speak  of.  Many  of  them  consider  A.  B  as  adopting 
the  spirit-hypothesis.  The  whole  book  was  written,  as  both  the 
authors  point  out,  to  suggest  inquiry  to  those  who  are  curious ; 
C.  D.  firmly  believing,  A.  B.  as  above.  Neither  C.  D.  nor  A.  B. 
make  any  other  pretence.  Both  dwell  upon  the  absence  of 
authentications  and  the  suppression  of  names  as  utterly  preven- 
tive of  anything  like  proof.  And  A.  B.  says  that  his  reader  '  will 
give  him  credit,  if  not  himself  a  goose,  for  seeing  that  the 
tender  of  an  anonymous  cheque  would  be  of  equal  effect,  whether 
drawn  on  the  Bank  of  England  or  on  Aldgate  Pump.'  By  this 
test  a  number  of  the  reviewers  are  found  to  be  geese  :  for  they 
take  the  authors  as  offering  proof,  and  insist,  against  the  authors, 
on  the  very  point  on  which  the  authors  had  themselves  insisted 
beforehand. 

Leaving  aside  imperceptions  of  this  kind,  I  proceed  to  notice  a 
clerical  and  medical  review.  I  have  lived  much  in  the  middle 
ages,  especially  since  the  invention  of  printing  ;  and  from  thence 
I  have  brought  away  a  high  respect  for  and  grateful  recollection 
of — the  priest  in  everything  but  theology,  and  the  physician  in 
everything  but  medicine.  The  professional  harness  was  unfavour- 


382  A  BUDGET   OF  PARADOXES. 

able  to  all  progress,  except  on  a  beaten  road ;  the  professional 
blinkers  prevented  all  but  the  beaten  road  from  being  seen  :  the 
professional  reins  were  pulled  at  the  slightest  attempt  to  quicken 
pace,  even  on  the  permitted  path  ;  and  the  professional  whip  was 
heavily  laid  on  at  the  slightest  attempt  to  diverge.  But  when 
the  intelligent  man  of  either  class  turned  his  attention  out  of  his 
ordinary  work,  he  had,  in  most  cases,  the  freshness  and  vigour  of 
a  boy  at  play,  and  like  the  boy,  he  felt  his  freedom  all  the  more 
from  the  contrast  of  school-restraint. 

In  the  case  of  medicine,  and  physics  generally,  the  learned 
were,  in  some  essential  points,  more  rational  than  many  of  their 
present  impugners.  They  pass  for  having  put  a  priori  obstacles 
in  the  way  of  progress  :  they  might  rather  be  reproved  for  too 
much  belief  in  progress  obtained  by  a  priori  means.  They 
would  have  shouted  with  laughter  at  a  dunce  who — in  a  review  I 
read,  but  without  making  a  note — declared  that  he  would  not 
believe  his  senses  except  when  what  they  showed  him  was  capable 
of  explanation  upon  some  known  principle.  I  have  seen  such 
stuff  as  this  attributed  to  the  schoolmen  ;  but  only  by  those  who 
knew  nothing  about  them.  The  following,  which  I  wrote  some 
years  ago,  will  give  a  notion  of  a  distinction  worth  remembering. 
It  is  addressed  to  the  authorities  of  the  College  of  Physicians. 

"  The  ignominy  of  the  word  empiric  dates  from  the  ages  in 
which  scholastic  philosophy  deduced  physical  consequences  a 
priori  ; — the  ages  in  which,  because  a  lion  is  strong,  rubbing  with 
lion's  fat  would  have  been  held  an  infallible  tonic.  In  those 
happy  days,  if  a  physician  had  given  decoction  of  a  certain  bark, 
only  because  in  numberless  instances  that  decoction  had  been 
found  to  strengthen  the  patient,  he  would  have  been  a  miserable 
empiric.  Not  that  the  colleges  would  have  passed  over  his  re- 
turns because  they  were  empirical :  they  knew  better.  They 
were  as  skilful  in  finding  causes  for  facts,  as  facts  for  causes. 
The  president  and  the  elects  of  that  day  would  have  walked  out  into 
the  forest  with  a  rope,  and  would  have  pulled  heartily  at  the  tree 
which  yielded  the  bark  :  nor  would  they  ever  have  left  it  until 
they  had  pulled  out  a  legitimate  reason.  If  the  tree  had  resisted 
all  their  efforts,  they  would  have  said  '  Ah  !  no  wonder  now  ;  the 
bark  of  a  strong  tree  makes  a  strong  man.'  But  if  they  had 
managed  to  serve  the  tree  as  you  would  like  to  serve  homoeopathy 
then  it  would  have  been  *  We  might  have  guessed  it ;  all  the 
virtus  roborativa  has  settled  in  the  bark.'  They  admitted,  as  we 
know  from  Moliere,  the  virtus  dormitiva  of  opium,  for  no  other 
reason  than  that  opium  facit  dormire.  Had  the  medicine  not 


REVIEWS  OF   '  FROM  MATTER  TO  SPIRIT.'  383 

been  previously  known,  they  would,  strange  as  it  may  seem  to 
modern  pharmacopoeists,  have  accorded  a  virtus  domnitiva  to  the 
new  facit  dormire.  On  this  point  they  have  often  been  misap- 
prehended. They  were  prone  to  infer  facit  from  a  virtus  ima- 
gined a  priori  ;  and  they  were  ready  in  supplying  facit  in  favour 
of  an  orthodox  virtus.  They  might  have  gone  so  far,  for  example, 
under  pre-notional  impressions,  as  the  alliterative  allopath,  who, 
when  maintenance  of  truth  was  busy  opposing  the  progress  of 
science  called  vaccination,  declared  that  some  of  its  patients 
coughed  like  cows,  and  bellowed  like  bulls ;  but  they  never 
refused  to  find  virtus  when  facit  came  upon  them,  no  matter 
whence.  They  would  rather  have  accepted  Tenterden  steeple 
than  have  rejected  the  Goodwin  Sands.  They  would  have 
laughed  their  modern  imitators  to  scorn :  but  as  they  are  not 
here,  we  do  it  for  them. 

"  The  man  of  our  day — the  a  priori  philosopher — tries  the 
question  whether  opium  can  cause  sleep  by  finding  out  in  the 
recesses  of  his  own  noddle  whether  the  drug  can  have  a  dormitive 
power :  Well !  but  did  not  the  schoolman  do  the  same  ?  He 
did ;  but  mark  the  distinction.  The  schoolman  had  recourse  to 
first  principles,  when  there  was  no  opium  to  try  it  by :  our  man 
settles  the  point  in  the  same  way  with  a  lump  of  opium  before 
him.  The  schoolman  shifted  his  principles  with  his  facts :  the 
man  of  our  drawing-rooms  will  fight  facts  with  his  principles, 
just  as  an  old  physician  would  have  done  in  actual  practice,  with 
the  rod  of  his  Church  at  his  back. 

"  The  story  about  Galileo — which  seems  to  have  been  either  a 
joke  made  against  him,  or  by  him — illustrates  this.  Nature 
abhors  a  vacuum  was  the  explanation  of  the  water  rising  in  a 
pump :  but  they  found  that  the  water  would  not  rise  more  than 
32  feet.  They  asked  for  explanation :  what  does  the  satirist 
make  the  schoolmen  say  ?  That  the  stoppage  is  not  a  fact,  be- 
cause nature  abhors  a  vacuum  ?  No  !  but  that  the  principle 
should  be  that  nature  abhors  a  vacuum  as  far  as  32  feet.  And 
this  is  what  would  have  been  done. 

"  There  are  still  among  us  both  priests  and  physicians  who  would 
have  belonged,  had  they  lived  three  or  four  centuries  ago,  to  the 
glorious  band  of  whom  I  have  spoken,  the  majority  of  the  intelli- 
gent, working  well  for  mankind  out  of  the  professional  pursuit. 
But  we  have  a  great  many  who  have  helped  to  abase  their  classes. 
Go  where  we  may,  we  find  specimens  of  the  lower  orders  of  the 
ministry  of  religion  and  the  ministry  of  health  showing  them- 
selves smaller  than  the  small  of  other  pursuits.  And  how  is  this  ? 


384  A   BUDGET   OF  PARADOXES. 

First,  because  each  profession  is  entered  upon  a  mere  working 
smack  of  its  knowledge,  without  any  depth  of  education,  general 
or  professional.  Not  that  this  is  the  whole  explanation,  nor  in 
itself  objectionable  :  the  great  mass  of  the  world  must  be  tended, 
soul  and  body,  by  those  who  are  neither  Hookers  nor  Harveys : 
let  such  persons  not  venture  ultra  crepidam,  and  they  are  useful 
and  respectable.  But,  secondly,  there  is  a  vast  upheaving  of 
thought  from  the  depths  of  commonplace  learning.  I  am  a 
clergyman !  Sir !  I  am  a  medical  man !  Sir !  and  forthwith  the 
nature  of  things  is  picked  to  pieces,  and  there  is  a  race,  with  the 
last  the  winner,  between  Philosophy  mounted  on  Folly's  donkey, 
and  Folly  mounted  on  Philosophy's  donkey.  How  fortunate  it  is 
for  Law  that  her  battles  are  fought  by  politicians  in  the  Houses 
of  Parliament.  Not  that  it  is  better  done :  but  then  politics 
bears  the  blame." 

I  now  come  to  the  medical  review.  After  a  quantity  of  remark 
which  has  been  already  disposed  of,  the  writer  shows  Greek 
learning,  a  field  in  which  the  old  physician  would  have  had  a 
little  knowledge.  A.  B.,  for  the  joke's  sake,  had  left  untranslated, 
as  being  too  deep,  a  remarkably  easy  sentence  of  Aristotle,  to  the 
effect  that  what  has  happened  was  possible,  for  if  impossible  it 
would  not  have  happened.  The  reviewer,  in  '  simple  astonish- 
ment,'— it  was  simple — at  the  pretended  incapacity — I  was  told 
by  A.  B.  that  the  joke  was  intended  to  draw  out  a  reviewer — 
translates  : — He  says  that  this  sentence  is  A.  B.'s  summing  up  of 
the  evidence  of  Spiritualism.  Now,  being  a  sort  of  alter  ego  of 
A.  B.,  I  do  declare  that  he  is  not  such  a  fool  as  to  rest  the  evidence 
of  Spiritualism — the  spirit  explanation — upon  the  occurrence  of 
certain  facts  proving  the  possibility  of  those  very  facts.  In  truth, 
A.  B.  refuses  to  receive  spiritualism,  while  he  receives  the  facts  : 
this  is  the  gist  of  his  whole  preface,  which  simply  admits  spirit- 
ualism among  the  qualified  candidates,  and  does  not  know  what 
others  there  may  be. 

The  reviewer  speaks  of  Aristotle  as  'that  clear  thinker  and 
concise  writer.'  I  strongly  suspect  that  his  knowledge  of  Aris- 
totle was  limited  to  the  single  sentence  which  he  had  translated 
or  got  translated.  Aristotle  is  concise  in  phrase,  not  in  book, 
and  is  powerful  and  profound  in  thought :  but  no  one  who  knows 
that  his  writing,  all  we  have  of  him,  is  the  very  opposite  of  clear, 
will  pretend  to  decide  that  he  thought  clearly.  As  his  writing, 
so  probably  was  his  thought ;  and  his  books  are,  if  not  anything 
but  clear,  at  least  anything  good  but  clear.  Nobody  thinks  them 
clear  except  a  person  who  always  clears  difficulties :  which  I  have 


REVIEWS  OF  c  FROM  MATTER  TO  SPIRIT.'        385 

no  doubt  was  the  reviewer's  habit ;  that  is,  if  he  ever  took  the 
field  at  all.  The  gentleman  who  read  Euclid,  all  except  the  As  and 
Bs  and  the  pictures  of  scratches  and  scrawls,  is  the  type  of  a 
numerous  class. 

The  reviewer  finds  that  the  word  amosgepotically,  used  by  A.  B., 
is  utterly  mysterious  and  incomprehensible.  He  hopes  his  trans- 
lation of  the  bit  of  Greek  will  shield  him  from  imputation  of 
ignorance  :  and  thinks  the  word  may  be  referred  to  the  '  obscure 
dialect'  out  of  which  sprung  aneroid,  kalos  geusis  sauce,  and 
Anaxyridian  trousers.  To  lump  the  first  two  phrases  with  the 
third  smacks  of  ignorance  in  a  Greek  critic  ;  for  dva^vpiSta,  breeches, 
would  have  turned  up  in  the  lexicon ;  and  kalos  geusis,  though 
absurd,  is  not  obscure.  And  a/i&>cr<ye7r&>s,  somehow  or  other,  is 
as  easily  found  as  dva^vpiBia.  The  word  aneroid,  I  admit, 
has  puzzled  better  scholars  than  the  critic :  but  never  one  who 
knows  the  unscholarlike  way  in  which  words  ending  in  siSrjs  have 
been  rendered.  The  aneroid  barometer  does  not  use  a  column  of 
air  in  the  same  way  as  the  old  instrument.  Now  dsposiSrjs — 
properly  like  the  atmosphere — is  by  scientific  non-scholarship 
rendered  having  to  do  with  the  atmosphere  ;  and  avaeposiSrjs — say 
anaeroid — denies  having  to  do  with  the  atmosphere  ;  a  nice  thing 
to  say  of  an  instrument  which  is  to  measure  the  weight  of  the 
atmosphere.  One  more  absurdity,  and  we  have  aneroid,  and 
there  you  are.  The  critic  ends  with  a  declaration  that  nothing 
in  the  book  shakes  his  faith  in  a  Quarterly  reviewer  who  said 
that  suspension  of  opinion,  until  further  evidence  arrives,  is 
justifiable  :  a  strange  summing  up  for  an  article  which  insists 
upon  utter  rejection  being  unavoidable.1  The  expressed  aim  of 
both  A.  B.  and  C.  D.  was  to  excite  inquiry,  and  get  further 
evidence  :  until  this  is  done,  neither  asks  for  a  verdict. 

Oh  where !  and  oh  where !  is  old  Medicine's  learning  gone  I 
There  was  some  in  the  days  of  yore,  when  Popery  was  on  I  And 
it's  oh  !  for  some  Greek,  just  to  find  a  word  upon  !  The  reviewer 
who,  lexicon  in  hand,  can  neither  make  out  anaxyridical,  araos- 
gepotical,  kalos  geusis,  nor  distinguish  them  from  aneroid,  cannot 
be  trusted  when  he  says  he  has  translated  a  sentence  of  Aristotle. 
He  may  have  done  it ;  but,  as  he  says  of  spiritualism,  we  must 
suspend  our  opinion  until  further  evidence  shall  arrive. 

\Ve  now  come  to  the  theological  review.  I  have  before  alluded 
to  the  faults  of  logic  which  are  Protestant  necessities  :  but  I  never 
said  that  Protestant  argument  had  nothing  but  paralogism.  The 

1  Tliis  "  utter  rejection"  lias  been  repeated  (1872)  by  the  same  writer. — El). 

C  G 


386  A  BUDGET   OF  PARADOXES. 

writer  before  me  attains  this  completeness :  from  beginning  to 
end  he  is  of  that  confusion  and  perversion  which,  as  applied  to 
interpretation  of  the  New  Testament,  is  so  common  as  to  pass 
unnoticed  by  sermon-hearers ;  but  which,  when  applied  out  of 
church,  is  exposed  with  laughter  in  all  subjects  except  theology. 
I  shall  take  one  instance,  putting  some  words  in  italics. 

A.  B.  Theological  Critic. 

My  state  of  mind,  which  refers  ...  he  proceeds  to  argue   that 

the  whole  either  to  unseen  intelli-  he  himself  is   outside  its  sacred 

gence,  or  something  which  man  has  pale   because  he  refers  all  these 

never  had  any  conception  of,  proves  strange    phenomena     to     unseen 

me  to  be  out  of  the  pale  of  the  spiritual  intelligence. 
Royal  Society. 

The  possibility  of  a  yet  unimagined  cause  is  insisted  on  in 
several  places.  On  this  ground  it  is  argued  by  A.  B.  that 
spiritualists  are  '  incautious '  for  giving  in  at  once  to  the  spirit 
doctrine.  But,  it  is  said,  they  may  be  justified  by  the  philo- 
sophers,-who  make  the  flint  axes,  as  they  call  them,  to  be  the 
works  of  men,  because  no  one  can  see  what  else  they  can  be.  This 
kind  of  adoption,  condemned  as  a  conclusion,  is  approved  as  a 
provisional  theory,  suggestive  of  direction  of  inquiry :  experience 
having  shown  that  inquiry  directed  by  a  wrong  theory  has  led  to 
more  good  than  inquiry  without  any  theory  at  all.  All  this  A.  B. 
has  fully  set  forth,  in  several  pages.  On  it  the  reviewer  remarks 
that  i  with  infinite  satisfaction  he  tries  to  justify  his  view  of  the 
case  by  urging  that  there  is  no  other  way  of  accounting  for  it ; 
after  the  fashion  of  the  philosophers  of  our  own  day,  who  conclude 
that  certain  flints  found  in  the  drift  are  the  work  of  men,  because 
the  geologist  does  not  see  what  else  they  can  be.'  After  this 
twist  of  meaning,  the  reviewer  proceeds  to  say,  and  A.  B.  would 
certainly  join  him,  '  There  is  no  need  to  combat  any  such  mode  of 
reasoning  as  this,  because  it  would  apply  with  equal  force  and 
justice  to  any  theory  whatever,  however  fantastic,  profane,  or  silly.' 
And  so,  having  shown  how  the  reviewer  has  hung  himself,  I  leave 
him  funipendulous. 

One  instance  more,  and  I  have  done.  A  reviewer,  not  theologi- 
cal, speaking  of  the  common  argument  that  things  which  are 
derided  are  not  therefore  to  be  rejected,  writes  as  follows  : — '  It 
might  as  well  be  said  that  they  who  laughed  at  Jenner  and  vacci- 
nation were,  in  a  certain  but  very  unsatisfactory  way,  witnesses  to 
the  possible  excellence  of  the  system  of  St.  John  Long.'  Of  course 
it  might :  and  of  course  it  is  said  by  all  people  of  common  sense. 
In  introducing  the  word  '  possible,'  the  reviewer  has  hit  the  point : 
I  suspect  that  this  word  was  introduced  during  revision,  to  put 


REVIEWS  OF  'FROM  MATTER   TO   SPIRIT.'  387 

the  sentence  into  fighting  order,  hurry  preventing  it  being  seen 
that  the  sentence  was  thus  made  to  fight  on  the  wrong  side. 
Jenner,  who  was  laughed  at,  was  right ;  therefore,  it  is  not  im- 
possible— that  is,  it  is  possible — that  a  derided  system  may  be 
right.  Mark  the  three  gradations  :  in  medio  tutissimus  ibis. 

Reviewer. — If  a  system  be  derided,  it  is  no  ground  of  suspense 
that  derided  systems  have  turned  out  true :  if  it  were,  you  would 
suspend  your  opinion  about  St.  John  Long  on  account  of  Jenner. 
— Ans.  You  ought  to  do  so,  as  to  possibility ;  and  before  examina- 
tion ;  not  with  the  notion  that  J.  proves  St.  J.  probable ;  only 
possible. 

Common  Sense. — The  past  emergence  of  truths  out  of  derided 
systems  proves  that  there  is  a  practical  certainty  of  like  occur- 
rence to  come.  But,  inasmuch  as  a  hundred  speculative  fooleries 
are  started  for  one  truth,  the  mind  is  permitted  to  approach  the 
examination  of  any  one  given  novelty  with  a  bias  against  it  of  a 
hundred  to  one :  and  this  permission  is  given  because  so  it  will 
be,  leave  or  no  leave.  Every  one  has  licence  not  to  jump  over 
the  moon. 

Paradoxer. — Great  men  have  been  derided,  and  I  am  derided  : 
which  proves  that  my  system  ought  to  be  adopted.  This  is  a 
summary  of  all  the  degrees  in  which  paradoxers  contend  for  the 
former  derision  of  truths  now  established,  giving  their  systems 
probability.  I  annex  a  paragraph  which  D  [e  &c.]  inserted  in 
the  Athenceum  of  October  23,  1847. 

"DISCOVERERS  AND   DISCOVERIES. 

"  Aristotle  once  sent  his  servant  to  the  cellar  to  fetch  wine  ; — 
and  the  fellow  brought  him  back  small  beer.  The  Stagirite  (who 
knew  the  difference)  called  him  a  blockhead.  '  Sir,'  said  the  man, 
*  all  I  can  say  is,  that  I  found  it  in  the  cellar.'  The  philosopher 
muttered  to  himself  that  an  affirmative  conclusion  could  not  be 
proved  in  the  second  figure, — and  Mrs.  Aristotle,  who  was  by,  was 
not  less  effective  in  her  remark,  that  small  beer  was  not  wine 
because  it  was  in  the  same  cellar.  Both  were  right  enough  :  and 
our  philosophers  might  take  a  lesson  from  either — for  they 
insinuate  an  affirmative  conclusion  in  the  second  figure.  Great 
discoverers  have  been  little  valued  by  established  schools, — and 
they  are  little  valued.  The  results  of  true  science  are  strange  at 
ftr8t, — and  so  are  their's.  Many  great  men  have  opposed  existing 
notions, — and  so  do  they.  All  great  men  were  obscure  at  first, — 
and  they  are  obscure.  Thinking  men  doubt, —  and  they  doubt. 

c  c  2 


388  A  BUDGET  OF  PARADOXES. 

Their  small  beer,  I  grant,  has  come  out  of  the  same  cellar  as  the 
wine  ;  but  this  is  not  enough.  If  they  had  let  it  stand  awhile  in 
the  old  wine-casks,  it  might  have  imbibed  a  little  of  the  flavour." 

There  are  better  reviews  than  I  have  noticed  ;  which,  though 
entirely  dissenting,  are  unassailable  on  their  own  principles. 
What  I  have  given  represents  five-sixths  of  the  whole.  But  it 
must  be  confessed  that  the  fraction  of  fairness  and  moderation 
and  suspended  opinion  which  the  doctrine  of  Spirit  Manifestations 
has  met  with — even  in  the  lower  reviews — is  strikingly  large 
compared  what  would  have  been  the  case  fifty  years  ago.  It  is 
to  be  hoped  that  our  popular  and  periodical  literatures  are  giving 
us  one  thinker  created  for  twenty  geese  double-feathered  :  if  this 
hope  be  realised,  we  shall  do !  Seeing  all  that  I  see,  I  am  not 
prepared  to  go  the  length  of  a  friend  of  mine  who,  after  reading 
a  good  specimen  of  the  lower  reviewing,  exclaimed — Oh  !  if  all 
the  fools  in  the  world  could  be  rolled  up  into  one  fool,  what  a 
reviewer  he  would  make  ! 

Calendrier  Universel   et   Perpetual ;  par  le  Commandeur  P.  J. 

Arson.      Publie   par   ses   Enfans    (CEuvre   posthume).      Nice, 

1863,  4to. 

I  shall  not  give  any  account  of  this  curious  calendar,  with  all 
its  changes  and  symbols.  But  there  is  one  proposal,  which, 
could  we  alter  the  general  notions  of  time — a  thing  of  very 
dubious  possibility — would  be  convenient.  The  week  is  made  to 
wax  and  wane,  culminating  on  the  Sunday,  which  comes  in  the 
middle.  Thursday,  Friday,  Saturday,  are  ascending  or  waxing 
days ;  Monday,  Tuesday,  Wednesday,  are  descending  or  waning 
days.  Our  six  days,  lumped  together  after  the  great  distinguish- 
ing day,  Sunday,  are  too  many  to  be  distinctly  thought  of  to- 
gether :  a  division  of  three  preceding  and  three  following  the 
day  of  most  note  would  be  much  more  easily  used.  But  all  this 
comes  too  late.  It  may  be,  nevertheless,  that  some  individuals 
may  be  able  to  adjust  their  affairs  with  advantage  by  referring 
Thursday,  Friday,  Saturday,  to  the  following  Sunday,  and  Mon- 
day, Tuesday,  Wednesday,  to  the  preceding  Sunday,  But  M. 
Arson's  proposal  to  alter  the  names  of  the  days  is  no  more 
necessary  than  it  is  practicable. 


I  am  not  to  enter  anything  I  do  not  possess.  The  reader 
therefore  will  not  learn  from  me  the  feats  of  many  a  man-at-arms 
in  these  subjects.  He  must  be  content,  unless  he  will  bestir 


CYCLOMETRY.  389 

himself  for  himself,  not  to  kno^v  how  Mr.  Patrick  Cody  trisects 
the  angle  at  Mullinavat,  or  Professor  Eecalcati  squares  the  circle 
at  Milan.  But  this  last  is  to  be  done  by  subscription,  at  five 
francs  a  head :  a  banker  is  named  who  guarantees  restitution  if 
the  solution  be  not  perfectly  rigorous ;  the  banker  himself,  I 
suppose,  is  the  judge.  I  have  heard  of  a  man  of  business  who 
settled  the  circle  in  this  way :  if  it  can  be  reduced  to  a  debtor 
and  creditor  account,  it  can  certainly  be  done  ;  if  not,  it  is  not 
worth  doing.  Montucla  will  give  the  accounts  of  the  lawsuits 
which  wagers  on  the  problem  have  produced  in  France. 

Neither  will  I  enter  at  length  upon  the  success  of  the  new 
squarer  who  advertises  (Nov.  1863)  in  a  country  paper  that, 
having  read  that  the  circular  ratio  was  undetermined,  '  I  thought 
it  very  strange  that  so  many  great  scholars  in  all  ages  should 
have  failed  in  finding  the  true  ratio,  and  have  been  determined 
to  try  myself  ...  I  am  about  to  secure  the  benefit  of  the  dis- 
covery, so  until  then  the  public  cannot  know  my  new  and  true 
ratio.'  I  have  been  informed  that  this  trial  makes  the  diameter 
to  the  circumference  as  64  to  201,  giving  TT  =  3'140625  exactly. 
The  result  was  obtained  by  the  discoverer  in  three  weeks  after  he 
first  heard  of  the  existence  of  the  difficulty.  This  quadrator  has 
since  published  a  little  slip,  and  entered  it  at  Stationers'  Hall. 
He  says  he  has  done  it  by  actual  measurement ;  and  I  hear  from 
a  private  source  that  he  uses  a  disk  of  12  inches  diameter,  which 
he  rolls  upon  a  straight  rail.  Mr.  James  Smith  did  the  same  at 
one  time  ;  as  did  also  his  partisan  at  Bordeaux.  We  have,  then, 
both  3*125  and  3-140625,  by  actual  measurement.  The  second 
result  is  more  than  the  first  by  about  one  part  in  200.  The 
second  rolling  is  a  very  creditable  one  ;  it  is  about  as  much  below 
the  mark  as  Archimedes  was  above  it.  Its  performer  is*a  joiner, 
who  evidently  knows  well  what  he  is  about  when  he  measures ; 
he  is  not  wrong  by  1  in  3,000. 

The  reader  will  smile  at  the  quiet  self-sufficiency  with  which 
4 1  have  been  determined  to  try  myself  follows  the  information 
that  '  so  many  great  scholars  in  all  ages '  have  failed.  It  is  an 
admirable  spirit,  when  accompanied  by  common  sense  and  un- 
common self-knowledge.  When  I  was  an  undergraduate  there 
was  a  little  attendant  in  the  library  who  gave  me  the  following, — 
'  As  to  cleaning  this  library,  Sir,  if  I  have  spoken  to  the  Master 
once  about  it,  I  have  spoken  fifty  times  :  but  it  is  of  no  use  ;  he 
will  not  employ  littery  men ;  and  so  I  am  obliged  to  look  after  it 
myself.' 

I  do  not  think  I  have  mentioned  the  bright  form  of  quadrature 


390  A   BUDGET   OF  PARADOXES. 

in  which  a  square  is  made  equal  to  a  circle  by  making  each  side 
equal  to  a  quarter  of  the  circumference.  The  last  squarer  of  this 
kind  whom  I  have  seen  figures  in  the  last  number  of  the 
Athenceum  for  1855 :  he  says  the  thing  is  no  longer  a  problem, 
but  an  axiom.  He  does  not  know  that  the  area  of  the  circle  is 
greater  than  that  of  any  other  figure  of  the  same  circuit.  This 
any  one  might  see  without  mathematics.  How  is  it  possible  that 
the  figure  of  greatest  area  should  have  any  one  length  in  its 
circuit  unlike  in  form  to  any  other  part  of  the  same  length  ? 

The  feeling  which  tempts  persons  to  this  problem  is  that 
which,  in  romance,  made  it  impossible  for  a  knight  to  pass  a 
castle  which  belonged  to  a  giant  or  an  enchanter.  I  once  gave 
a  lecture  on  the  subject :  a  gentleman  who  was  introduced 
to  it  by  what  I  said  remarked,  loud  enough  to  be  heard  by  all 
around,  '  Only  prove  to  me  that  it  is  impossible,  and  I  will  set 
about  it  this  very  evening.' 

This  rinderpest  of  geometry  cannot  be  cured,  when  once  it  has 
seated  itself  in  the  system  :  all  that  can  be  done  is  to  apply  what 
the  learned  call  prophylactics  to  those  who  are  yet  sound.  When 
once  the  virus  gets  into  the  brain,  the  victim  goes  round 
the  flame,  like  a  moth,  first  one  way  and  then  the  other,  be- 
ginning again  where  he  ended,  and  ending  where  he  begun :  thus 
verifying  the  old  line 

In  giriim  imus  nocte,  ecce  !  et  consumimur  igni. 

Every  mathematician  knows  that  scores  of  methods,  differing 
altogether  from  each  other  in  process,  all  end  in  this  mys- 
terious 3-14159  .  .  .,  which  insists  on  calling  itself  the  circum- 
ference to  a  unit  of  diameter.  A  reader  who  is  competent  to 
follow  processes  of  arithmetic  may  be  easily  satisfied  that  such 
methods  do  actually  exist.  -  I  will  give  a  sketch,  carried  out  to 
a  few  figures,  of  three :  the  first  two  I  never  met  with  in  my 
reading ;  the  third  is  the  old  method  of  Vieta.  [I  find  that  both 
the  first  and  second  methods  are  contained  in  a  theorem  of 
Euler.] 

What  Mr.  James  Smith  says  of  these  methods  is  worth  noting. 
He  says  I  have  given  three  '  fancy  proofs'  of  the  value  of  TT  :  he 
evidently  takes  me  to  be  offering  demonstration.  He  proceeds 
thus : — 

'His  first  proof  is  traceable  to  the  diameter  of  a  circle  of  radius  1. 
His  second,  to  the  side  of  any  inscribed  equilateral  triangle  to  a  circle 
of  radius  X.  His  third,  to  a  radius  of  a  circle  of  diameter  1.  Now,  ifc 
be  frankly  admitted  that  we  can  arrive  at  the  same  result  by 


CYCLOMETRY.  391 

many  other  modes  of  arithmetical  calculation,  all  of  which  may  be 
shown  to  have  some  sort  of  relation  to  a  circle ;  but,  after  all,  these 
results  are  mere  exhibitions  of  the  properties  of  numbers,  and  have  no 
more  to  do  with  the  ratio  of  diameter  to  circumference  in  a  circle  than 
the  price  of  sugar  with  the  mean  height  of  spring  tides.  (Corr. 
Oct.  21,  1865).' 

I  quote  this  because  it  is  one  of  the  few  cases — other  than 
absolute  assumption  of  the  conclusion — in  which  Mr.  Smith's  con- 
clusions would  be  true  if  his  premise  were  true.  Had  I  given 
what  follows  as  proof ,  it  would  have  been  properly  remarked, 
that  I  had  only  exhibited  properties  of  numbers.  But  I  took 
care  to  tell  my  reader  that  I  was  only  going  to  show  him  methods 
which  end  in  3'14159  .  .  .  The  proofs  that  these  methods  establish 
the  value  of  TT  are  for  those  who  will  read  and  can  understand. 

1.  Take  any  diameter,  double  it,  take  l-3rd  of  that  double, 
2-5ths  of  the  last,  3-7ths  of  the  last,  4-9ths  of  the  last,  5-llths 
of  the  last,  and  so  on.  The  sum  of  all  is  the  circumference  of 
that  diameter.  The  following  is  the  process  when  the  diameter 
is  a  hundred  millions :  the  errors  arising  from  rejection  of 
fractions  being  lessened  by  proceeding  on  a  thousand  millions, 
and  striking  off  one  figure. 

200000000  31415    3799 

66666667  2817 

26666667  1363 

11428571  661 

5079365  321 

2308802  156 

1065601  76 

497281  37 

'   234014  18 

110849  9 

52785  5 

25245  2 

12118  1 

5834 


314153799  31415     9265 

Here  200  &c.  is  double  of  the  diameter ;  666  &c.  is  l-3rd  of 
200  &c. ;  266  &c.  is  2-5ths  of  666  &c. ;  114  &c.  is  3-7ths  of 
266  &c. ;  507  &c.  is  4-9ths  of  114  &c. ;  and  so  on. 

2.  To  the  square  root  of  3  add  its  half.  Take  half  the  third 
part  of  this ;  half  2-5ths  of  the  last ;  half  3-7 ths  of  the  last ;  and 
so  on.  The  sum  is  the  circumference  to  a  unit  of  diameter. 


392  A   BUDGET   OF  PARADOXES. 

Square  root  of  3  ....  1-  73205081 
•86602540 


2-59807621 

•43301270 

•08660254 

1855768 

412393 

93726 

21629 

5047 

1188 

281 

67 

16 

4 

1 


314159265 

3.  Take  the  square  root  of  ^ ;  the  square  root  of  half  of  one 
more  than  this  ;  the  square  root  of  half  of  one  more  than  the 
last ;  and  so  on,  until  we  come  as  near  to  unity  as  the  number  of 
figures  chosen  will  permit.  Multiply  all  the  results  together, 
and  divide  2  by  the  product :  the  quotient  is  an  approximation 
to  the  circumference  when  the  diameter  is  unity.  Taking  aim 
at  four  figures,  that  is,  working  to  five  figures  to  secure  accuracy 
in  the  fourth,  we  have  '70712  for  the  square  root  of  \ ;  '92390 
for  the  square  root  of  half  one  more  than  '70712  ;  and  so  on, 
through  -98080,  -99520,  -99880,  -99970,  -99992,  and  -99998.  The 
product  of  the  eight  results  is  '63667  ;  divide  2  by  this,  and  the 
quotient  is  3-1413  .  .  .,  of  which  four  figures  are  correct.  Had 
the  product  been  '636363  .  .  .  instead  of  '63667  .  .  .,  the  famous 
result  of  Archimedes,  22-7ths,  would  have  been  accurately  true. 
It  is  singular  that  no  cyclometer  maintains  that  Archimedes  hit 
it  exactly. 

A  literary  journal  could  hardly  admit  as  much  as  the  preceding, 

if  it  stood  alone.     But  in  my  present  undertaking  it  passes  as  the 

halfpennyworth  of  bread  to   many  gallons  of  sack.     Many  more 

x  methods  might  be  given,  all  ending  in  the  same  result,  let  that 

result  mean  what  it  may. 

Now  since  dozens  of  methods,  to  which  dozens  more  might  be 
added  at  pleasure,  concur  in  giving  one  and  the  same  result ; 
and  since  these  methods  are  declared  by  all  who  have  shown 
knowledge  of  mathematics  to  be  demonstrated :  it  is  not  asking 


CYCLOMETRY. 

too  much  of  a  person  who  has  just  a  little  knowledge  of  the  first 
elements  that  he  should  learn  more,  and  put  his  hand  upon  the 
error,  before  he  intrudes  his  assertion  of  the  existence  of  error 
upon  those  who  have  given  more  time  and  attention  to  it  than 
himself,  and  who  are  in  possession,  over  and  above  many  demon- 
strations, of  many  consequences  verifying  each  other,  of  which  he 
can  know  nothing.  This  is  all  that  is  required.  Let  any  one 
square  the  circle,  and  persuade  his  friends,  if  he  and  they  please : 
let  him  print,  and  let  all  read  who  choose.  But  let  him  abstain 
from  intruding  himself  upon  those  who  have  been  satisfied  by 
existing  demonstration,  until  he  is  prepared  to  lay  his  finger  on 
the  point  in  which  existing  demonstration  is  wrong.  Let  him 
also  say  what  this  mysterious  3'14159...  really  is,  which  comes  in 
at  every  door  and  window,  and  down  every  chimney,  calling  itself 
the  circumference  to  a -unit  of  diameter.  This  most  impudent 
and  successful  impostor  holds  false  title-deeds  in  his  hands,  and 
invites  examination :  surely  those  who  can  find  out  the  rightful 
owner  are  equally  able  to  detect  the  forgery.  All  the  quadrators 
are  agreed  that,  be  the  right  what  it  may,  3*14159...  is  wrong. 
It  would  be  well  if  they  would  put  their  heads  together,  and  say 
what  this  wrong  result  really  means.  The  mathematicians  of  all 
ages  have  tried  all  manner  of  processes,  with  one  object  in  view, 
and  by  methods  which  are  admitted  to  yield  demonstration  in 
countless  cases.  They  have  all  arrived  at  one  result.  A  large 
number  of  opponents  unite  in  declaring  this  result  wrong,  and 
all  agree  in  two  points  :  first,  in  differing  among  themselves  ; 
secondly,  in  declining  to  point  out  what  that  curious  result 
really  is  which  the  mathematical  methods  all  agree  in  giving. 

Most  of  the  quadrators  are  not  aware  that  it  has  been  fully 
demonstrated  that  no  two  numbers  whatsoever  can  represent  the 
ratio  of  the  diameter  to  the  circumference  with  perfect  accuracy. 
When  therefore  we  are  told  that  either  8  to  25  or  64  to  201  is 
the  true  ratio,  we  know  that  it  is  no  such  thing,  without  the 
necessity  of  examination.  The  point  that  is  left  open,  as  not 
fully  demonstrated  to,  be  impossible,  is  the  geometrical  quadra- 
ture, the  determination  of  the  circumference  by  the  straight  line 
and  circle,  used  as  in  Euclid.  The  general  run  of  circle- 
s'[imrers,  hearing  that  the  quadrature  is  not  pronounced  to  be 
demonstratively  impossible,  imagine  that  the  arithmetical  quad- 
rature is  open  to  their  ingenuity.  Before  attempting  the 
arithmetical  problem,  they  ought  to  acquire  knowledge  enough 
to  read  Lambert's  demonstration  (last  given  in  Brewster's  trans- 
lation of  Legendre's  Geometry)  and,  if  they  can,  tu  refute  it.  [It 


294  A   BUDGET   OF   PARADOXES. 

will  be  given  in  an  Appendix.]  Probably  some  have  begun  in 
this  way,  and  have  caught  a  Tartar  who  has  refused  to  let  them 
go  :  I  have  never  heard  of  any  one  who,  in  producing  his  own 
demonstration,  has  laid  his  finger  on  the  faulty  part  of  Lambert's 
investigation.  This  is  the  answer  to  those  who  think  that  the 
mathematicians  treat  the  arithmetical  squarers  too  lightly,  and 
that  as  some  person  may  succeed  at  last,  all  attempts  should  be 
examined.  Those  who  have  so  thought,  not  knowing  that  there 
is  demonstration  on  the  point,  will  probably  admit  that  a  person 
who  contradicts  a  theorem  of  which  the  demonstration  has  been 
acknowledged  for  a  century  by  all  who  have  alluded  to  it  as  read 
by  themselves,  may  reasonably  be  required  to  point  out  the  error 
before  he  demands  attention  to  his  own  result. 

Apopempsis  of  the  Tutelaries. — Again  and  again  I  am  told 
that  I  spend  too  much  time  and  trouble  upon  my  two  tutelaries  : 
but  when  I  come  to  my  summing-up  I  shall  make  it  appear  that 
I  have  a  purpose.  Some  say  I  am  too  hard  upon  them  :  but  this 
is  quite  a  mistake.  Both  of  them  beat  little  Oliver  himself  in  the 
art  and  science  of  asking  for  more ;  but  without  Oliver's  excuse, 
for  I  had  given  good  allowance.  Both  began  with  me,  not  I  with 
them  :  and  both  knew  what  they  had  to  expect  when  they  applied 
for  a  second  helping. 

On  July  31,  the  Monday  after  the  publication  of  my  remarks 
on  my  666  correspondent,  I  found  three  notes  in  separate 
envelopes,  addressed  to  me  at  '  7  A,  University  College.'  When  I 
saw  the  three  new  digits  I  was  taken  rhythmopoetic,  as  follows — 

Here  's  the  Doctor  again  with  his  figs,  and  by  Heavens ! 
He  was  always  at  sixes,  and  now  he 's  at  sevens. 

To  understand  this  fully  the  reader  must  know  that  the  greater 
part  of  Apocalyptic  interpretation  has  long  been  condensed,  in 
my  mind,  into  the  Turkish  street-cry — In  the  name  of  the 
Prophet !  figs  1  I  make  a  few  extracts.  The  reader  will  observe 
that  Dr.  Thorn  grumbles  at  his  private  letters  being  publicly 
ridiculed.  A  man  was  summoned  for  a  glutolactic  assault ;  he 
complained  of  the  publication  of  his  proceeding  :  I  kicked  &c.  in 
confidence,  he  said. 

"  After  reading  your  last,  which  tries  in  every  way  to  hold  me  up  to 
public  ridicule  for  daring  to  write  you  privately  ['  that  you  would  be 
d— d,'  omitted  by  accident]  one  would  say,  Why  nave  anything  to  do 
with  such  a  testy  person  ?  [Wrong  word  ;  no  testy  person  can  manage 
cool  and  consecutive  ridicule.  Quaere,  what  is  this  word  ?  Is  it  any- 
thing but  a  corruption  of  the  obsolete  word  tetchy  of  the  same  meaning  ? 


THE   SUMMER   OF   THE   I! EAST.  895 

Some  think  touchy  is  our  modern  form  of  tetchy,  which  I  greatly  doubt]. 

My  answer  is,  the  poor  man  is  lamentably  ignorant ;  he  is  not  only  so, 

bat  '  out  of  the  way  '  [quite  true  ;  my  readers  know  me  by  this  time 

for  an  out-of-the-way  person.     What  other  could  tackle  my  squad  of 

paradoxers  ?     What  other  would   undertake  the  job  ?].     Can  he  be 

brought  back  and  form  one  of  those  who  in  Ezekiel   37  ch.  have  the 

Spirit  breathed  into  them  and  live  .  .   .  Have  I  any  other  feeling 

towards  you  except  that  of  peace  and  goodwill  ?     [Not  to  your  distinct 

knowledge  ;  but  in  all  those  who   send  people  to  '  the  other  place  '  for 

contempt  of  their  interpretations,  there  is  a  lurking  wish  which  is 

father  to  the   thought ;  '  you  will  be  d — d '  and  you    ~be  d — d  '  are 

Siamese  twins].     Of  course  your  sneer  at  660  brought  plain  words ; 

but  when  men  meddle  with  what  they  do  not  understand  (not  having 

the  double   Valiu)  they  must  be  dealt   with  faithfully  by  those  who 

do  ...   [They  must ;  which  justifies  the  Budget  of  Paradoxes  :  but 

no  occasion  to  send  them  anywhere  ;  no  preachee  and  floggee  too,  as 

the  negro  said].     Many  will  find  the  text  Prov.  i.  26  fully  realized. 

[All  this  contains  distinct  assumption  of  a  right  '  of  course  '  to  declare 

accursed  those  who  do  not  respect  the  writer's  vagary]  ...  If  I  could 

but  get  the  x,  the  Ox-head,  which  in  old  Hebrew  was  just  the  Latin 

Digamma,  F,  out  of  your  name,  and  could  then  Thau  you  with  the  Thau 

of  Ezekiel  ix.  4,  the  x>  then  you  would  bear  the  number 

M       40     of  a  man  !     But  this  is  too  hard  for  me,  although  not  so 

O        70     for  the  Lord  !  Jer.  xxxii.  1 7  ...  And  now  a  word :  is 

R     100     ridicule  the  right  thing  in   so  solemn  a  matter  as  the 

G          6     discussion  of  Holy  Writ  ?     [Is  food  for  ridicule  the  right 

N       50     thing  ?     Did  I  discuss  Holy  Writ  ?     I  did  not :  I  con- 

cussed  profane  scribble.    Even  the  Doctor  did  not  discuss  : 

266     he  only  enunciated  and  denunciated  out  of  the  mass  of 
n  =  x   400     inferences  which  a  mystical  head  has  found  premises  for 
in  the  Bible]." 

[That  ill  opinions  are  near  relations  of  ill  wishes,  will  be 
detected  by  those  who  are  on  the  look  out.  The  following  was 
taken  down  in  a  Scotch  Church  by  Mr.  Cobden,  who  handed  it  to 
a  Roman  friend  of  mine,  for  his  delectation  (in  1855):  'Lord, 
we  thank  thee  that  thou  hast  brought  the  Pope  into  trouble ;  and 
we  pray  that  thou  wouldst  be  mercifully  pleased  to  increase  the 
same.'] 

Here  is  a  martyr  who  quarrels  with  his  crown  ;  a  missionary 
who  reviles  his  persecutor  :  send  him  to  New  Zealand,  and  he 
would  disagree  with  the  Maoris  who  ate  him.  Man  of  unilateral 
reciprocity !  have  you,  who  write  to  a  stranger  with  hints  that 
that  stranger  and  his  wife  are  children  of  perdition,  the  bad 
taste  to  complain  of  a  facer  in  return  ?  As  James  Smith — 


A   BUDGET   OF   PABADOXES. 

the    Attorney-wit,   not   the   Dock-cyclometer  —  said,    or   nearly 
said, 

"  A  pretty  thing,  forsooth  ! 
Is  he  to  burn,  all  scalding  hot, 
Me  and  my  wife,  and  am  I  not 
To  job  him  out  a  tooth  ?  " 

Those  who  think  parody  vulgar  will  be  pleased  to  substitute  for 
the  above  a  quotation  from  Butler : — 

There  's  nothing  so  absurd  or  vain, 

Or  barbarous  or  inhumane, 

But  if  it  lay  the  least  pretence 

To  piety  and  godliness, 

Or  tender-hearted  conscience, 

And  zeal  for  gospel  truths  profess, — 

Does  sacred  instantly  commence, 

And  all  that  dare  but  question  it  are  straight 

Pronounced  th'  uncircu  incised  and  reprobate. 

As  malefactors  that  escape  and  fly 

Into  a  sanctuary  for  defence, 

Must  not  be  brought  to  justice  thence, 

Although  their  crimes  be  ne'er  so  great  and  high. 

And  he  that  dares  presume  to  do't 

Is  sentenced  and  delivered  up 

To  Satan  that  engaged  him  to't. 

Of  all  the  drolleries  of  controversy  none  is  more  amusing  than 
the  manner  in  which  those  who  provoke  a  combat  expect  to  lay 
down  the  laws  of  retaliation.  You  must  not  strike  this  way  !  you 
must  not  parry  that  way !  If  you  don't  take  care,  we  shall  never 
meddle  with  you  again  !  We  were  not  prepared  for  such  as  this  ! 
Why  did  we  have  anything  to  do  with  such  a  testy  person  ?  M. 
Jourdain  must  needs  show  Nicole,  his  servant-maid,  how  good  a 
thing  it  was  to  be  sure  of  fighting  without  being  killed,  by  carte 
and  tierce  :  '  Et  cela  n'est  il  pas  beau  d'etre  assure  de  son  fait 
quand  on  se  bat  contre  quelqu'un  ?  La,  pousse  moi  un  peu,  pour 
voir.  NICOLE.  Eh  bien  !  quoi  ?  M.  JOUKDAIN.  Tout  beau.  Hola  I 
Ho !  doucement.  Diantre  soit  la  coquine !  NICOLE.  Vous  me 
dites  de  pousser.  M.  JOURDAIN.  Oui ;  mais  tu  me  pousses  en 
tierce,  avant  que  de  pousser  en  quarte,  et  tu  n'as  pas  la  patience 
qne  je  pare.' 

His  colleague,  my  secular  tutelary,  who  also  made  an  ana- 
chronistic onset,  with  his  repartees  and  his  retorts,  before  there  was 
anything  to  fire  at,  takes  what  I  give  by  way  of  subsequent  pro- 
vocation with  a  good  humour  which  would  make  a  convert  of  me 


THE  NUMBER  OF  THE  BEAST.  397 

if  he  could  afford  -01659265  ...  of  a  grain  of  logic.  He  instantly 
sent  me  his  photograph  for  the  asking,  and  another  letter  in 
proof.  The  Thor-hamraerer  does  nothing  but  grumble,  except 
when  he  tells  a  good  story,  which  he  says  he  had  from  Dr. 
Abernethy.  A  Mr.  James  Dunlop  was  popping  at  the  Papists 
with  a  666-rifled  gun,  when  Dr.  Chalmers  quietly  said,  '  Why, 
Dunlop,  you  bear  it  yourself,'  and  handed  him  a  paper  on  which 
the  numerals  in 

IACOBVS     DVNLOPVS 

1    100       5       500  5     50       5 

were  added  up.  This  is  almost  as  good  as  the  Filii  Dei  Vicarius, 
the  numeral  letters  of  which  also  make  666.  No  more  of  these 
crazy — I  first  wrote  puerile,  but  why  should  young  cricketers 
be  libelled  ? — attempts  to  extract  religious  use  from  numerical 
vagaries,  and  to  make  God  over  all  a  proposer  of  salvation  conun- 
drums :  and  no  more  of  the  trumpery  hints  about  future  destiny 
which  it  is  too  great  a  compliment  to  call  blasphemous.  If  the 
Doctor  will  cipher  upon  the  letters  in  sv  a>  fjbsrpa>  /Asrpsire  fj.£Tpij- 
B'TjasTai  vftiv,  with  double  Vahu  cubic  measure,  he  will  perhaps 
learn  to  leave  off  trying  to  frighten  me  into  gathering  grapes 
from  thorns. 

Mystical  hermeneutics  may  be  put  to  good  use  by  out-of-the- 
way  people.  They  may  be  made  to  call  the  attention  of  the 
many  to  a  distinction  well  known  among  the  learned.  The  books 
of  the  New  Testament  have  been  for  1,500  years  divided  into  two 
classes :  the  acknowledged  (o/ioA.o7ou/uera),  which  it  has  always 
been  paradox  not  to  receive  ;  and  the  controverted  (avTiXsyofjusva), 
about  which  there  has  always  been  that  difference  of  opinion 
which  no  scholar  overlooks,  however  he  may  decide  for  himself 
after  balance  of  evidence.  Eusebius,  who  first  (1.  3,  c.  25) 
recorded  the  distinction — which  was  much  insisted  on  by  the 
early  Protestants — states  the  books  which  are  questioned  as 
doubtful,  but  which  yet  are  approved  and  acknowledged  by  many 
— or  the  many,  it  is  not  easy  to  say  which  he  means — to  be  the 
Epistles  of  James  and  Jude,  the  second  of  Peter  and  the  second 
and  third  of  John.  In  other  places  he  speaks  doubtingly  of  the 
Epistle  to  the  Hebrews.  The  Apocalypse  he  does  not  even  admit 
into  this  class,  for  he  proceeds  as  follows — I  use  the  second  edition 
of  the  English  folio  translation  (1709),  to  avert  suspicion  of  bias 
from  myself: — 

'Among  the  spurious  [voQni]  let  there  be  ranked  both  the  work 
entitled  the  Acts  of  Paul,  and  the  book  called  Pastor,  and  the  Race- 


303  A   BUDGET   OF  PABADOXES. 

lalion  of  Peter :  and  moreover  that  which  is  called  the  Epistle  of 
Barnabas,  and  that  named  the  Doctrines  of  the  Apostles :  and  moreover, 
as  I  said,  the  Revelation  of  John  (if  you  think  good),  which  some,  as  I 
have  said,  do  reject,  but  others  allow  of,  and  admit  among  those  books 
which  are  received  as  unquestionable  and  undoubted.' 

Eusebius,  though  he  will  not  admit  the  Apocalypse  even  into 
the  controverted  list,  but  gives  permission  to  call  it  spurious, 
yet  qualifies  his  permission  in  a  manner  which  almost  annihilates 
the  distinctive  force  of  voOu?.,  and  gives  the  book  a  claim  to 
rank  (if  you  think  good,  again)  in  the  controverted  list.  And 
this  is  the  impression  received  by  the  mind  of  Lardner,  who  gives 
Eusebius  fully  and  fairly,  but  when  he  sums  up,  considers  his 
author  as  admitting  the  Apocalypse  into  the  second  list.  A  stick 
may  easily  be  found  to  beat  the  father  of  ecclesiastical  history. 
There  are  whole  faggots  in  writers  as  opposite  as  Baronius  and 
(ribbon,  who  are  perhaps  his  two  most  celebrated  sons.  But  we 
can  hardly  imagine  him  totally  misrepresenting  the  state  of 
opinion  of  those  for  whom  and  among  whom  he  wrote.  The  usual 
plan,  that  of  making  an  author  take  the  views  of  his  reader,  is 
more  easy  in  his  case  than  in  that  of  any  other  writer :  for,  as  the 
riddle  says,  he  is  You-see-by-us  ;  and  to  this  reading  of  his  name 
he  has  often  been  subjected.  Dr.  Nathaniel  Lardner,  who,  though 
heterodox  in  doctrine,  tries  hard  to  be  orthodox  as  to  the  Canon, 
is  '  sometimes  apt  to  tbink '  that  the  list  should  be  collected  and 
divided  as  in  Eusebius.  He  would  have  no  one  of  the  controverted 
books  to  be  allowed,  by  itself,  to  establish  any  doctrine.  Even 
without  going  so  far,  a  due  use  of  early  opinion  and  long  con- 
tinued discussion  would  perhaps  prevent  rational  people  from 
being  induced  by  those  who  have  the  double  Vahu  to  place  tbe 
Apocalypse  above  the  Gospels,  which  all  the  Bivahuites  do  in 
effect,  and  some  are  said  to  have  done  in  express  words.  But  my 
especial  purpose  is  to  point  out  that  an  easy  way  of  getting  rid  of 
665  out  of  666  of  tbe  mystics  is  to  require  them  to  establish  the 
Apocalypse  before  they  begin.  See  if  they  even  know  so  much 
as  that  there  is  a  crowd  of  testimonies  for  and  against,  running 
through  the  first  four  centuries,  which  makes  this  book  the  most 
difficult  of  tbe  whole  Canon.  Try  this  method,  and  you  will 
escape  beautiful,  as  the  French  say.  Dean  Alford,  in  vol.  iv.  p.  8. 
of  his  New  Testament,  gives  an  elaborate  handling  of  this  ques- 
tion. He  concludes  by  saying  that  he  cannot  venture  to  refuse 
his  consent  to  the  tradition  that  tbe  Apostle  is  the  author.  This 
modified  adherence,  or  non-noiiadherence,  pretty  well  represents 


APOCALYPTIC  PROPHECY.  399 

the  feeling  of  orthodox  Protestants,  when  learning  and  common 
sense  come  together. 

I  have  often,  in  former  days,  had  the  attempt  made  to  place 
the  Apocalypse  on  my  neck  as  containing  prophecies  yet  unfulfilled. 
The  preceding  method  prevents  success ;  and  so  does  the  follow- 
ing. It  may  almost  be  taken  for  granted  that  theological  system- 
fighters  do  not  read  the  New  Testament:  they  hunt  it  for 
detached  texts ;  they  listen  to  it  in  church  in  that  state  of 
quiescent  nonentity  which  is  called  reverent  attention  :  but  they 
never  read  it.  When  it  is  brought  forward,  you  must  pretend  to 
find  it  necessary  to  turn  to  the  book  itself:  you  must  read  '  The 
revelation  ...  to  show  unto  his  servants  things  which  must  shortly 
come  to  pass  ....  Blessed  is  he  that  readeth  ....  for  the  time 
is  at  hand.'  You  must  then  ask  your  mystic  whether  things 
deferred  for  1 800  years  were  shortly  to  come  to  pass,  &c.  ?  You 
must  tell  him  that  the  Greek  h  ra^si,  rendered  '  shortly,'  is  as 
stiong  a  phrase  as  the  language  has  to  signify  soon.  The  inter- 
preter will  probably  look  as  if  he  had  never  read  this  opening  : 
the  chances  are  that  he  takes  up  the  book  to  see  whether  you 
have  not  been  committing  a  fraud.  He  will  then  give  you  some 
exquisite  evasion  :  I  have  heard  it  pleaded  that  the  above  was  a 
mere  preamble.  This  word  mere  is  all-sufficient :  it  turns  any- 
thing into  nothing.  Perhaps  he  will  say  that  the  argument  is 
that  of  the  Papists  :  if  so,  tell  him  that  there  is  no  Christian  sect 
but  bears  true  witness  against  some  one  or  more  absurdities  in 
other  sects. 

An  anonyme  suggests  that  sv  ra^st  may  not  be  *  soon,'  it  may 
be  '  quickly,  without  reference  to  time  when  : '  he  continues  thus, 
4  May  not  time  be  "  at  hand  "  when  it  is  ready  to  come,  no  matter 
how  long  delayed  ? '  I  now  understand  what  *  *  *  and  *  *  * 
meant  when  they  borrowed  my  books  and  promised  to  return  them 
quickly,  it  was  '  without  reference  to  time  when.'  As  to  time  at 
hand — provided  you  make  a  long  arm — I  admire  the  quirk,  but 
cannot  receive  it :  the  word  is  eyyvs,  which  is  a  word  of  closeness, 
in  time,  in  place,  in  reckoning,  in  kindred,  &c. 

Another  gentleman  is  not  surprised  that  Apocalyptic  reading 
leads  to  a  doubt  of  the  '  canonicity '  of  the  book :  it  ought  not 
to  rest  on  church  testimony,  but  on  visible  miracle.  He  offers 
me,  or  any  reader  of  the  Atftenceum,  the  'sight  of  a  miracle  to 
that  effect,  and  within  forty-eight  hours'  journey  (fare  paid).'  I 
seldom  travel,  and  my  first  thought  was  whether  my  carpet-bag 
would  be  found  without  a  regular  hunt :  but,  on  reading  further,! 


400  A  BUDGET   OF  PARADOXES. 

found  that  it  was  only  a  concordance  that  would  be  wanted. 
Forty  hours'  collection  and  numerical  calculation  of  Grreek  nouns 
would  make  it — should  I  happen  to  agree  with  the  writer — many 
hundred  millions  to  one  that  Eevelation  xiii  is  superhuman. 
There  is  but  one  verse  (the  fifth)  which  the  writer  does  not  see 
verified.  I  looked  at  this  verse,  and  was  much  startled.  The 
Budget  began  in  October  1863:  should  it  last  until  March  1867 
— it  is  now  August  1866 — it  is  clear  that  I  am  the  first  Beast, 
and  my  paradoxers  are  the  saints  whom  I  persecute. 

[The  Budget  did  terminate  in  March  1867 :  I  hope  the 
gentleman  will  be  satisfied  with  the  resulting  interpretation.] 

The  same  opponent  is  surprised  that  I  should  suppose  a  thing 
which  '  comes  to  pass '  must  be  completed,  and  cannot  contain 
what  is  to  happen  1800  years  after.  All  who  have  any  know- 
ledge of  English  idiom  know  that  a  thing  comes  to  pass  when  it 
happens,  and  came  to  pass  afterwards.  But  as  the  original  is 
Greek,  we  must  look  at  the  Grreek  :  it  is  Ssi  jsvsadai  for  '  must 
come  to  pass,'  and  we  know  that  i^-vsro  is  what  is  usually  trans- 
lated 'came  to  pass.'  No  word  of  more  finished  completion 
exists  in  Grreek. 

And  now  for  a  last  round  of  biter-bit  with  the  Thor-hammerer, 
of  whom,  as  in  the  other  case,  I  shall  take  no  more  notice  until 
he  can  contrive  to  surpass  himself,  which  I  doubt  his  being  able 
to  do.  He  informs  me  that  by  changing  A  into  n  in  my  name 
he  can  make  a  666  of  me ;  adding,  '  This  is  too  hard  for  me, 
although  not  so  for  the  Lord  ! '  Sheer  nonsense  !  He  could  just 
as  easily  have  directed  to  '  Prof.  De  Morgnn '  as  have  assigned  me 
apartment  7A  in  University  College.  It  would  have  been  seen 
for  whom  it  was  intended :  and  if  not,  it  would  still  have  reached 
me,  for  my  colleagues  have  for  many  a  year  handed  all  out-of-the 
way  things  over  to  me.  There  is  no  7 A  :  but  7  is  the  Museum  of 
Materia  Medica.  I  took  the  only  hint  which  the  address  gave  : 
I  inquired  for  hellebore,  but  they  told  me  it  was  not  now  recog- 
nized, that  the  old  notion  of  its  value  was  quite  obsolete,  and. 
that  they  had  nothing  which  was  considered  a  specific  in  senary 
or  septenary  cases.  The  great  platitude  is  the  reference  of  such 
a  difficulty  as  writing  n  for  A  to  the  Almighty  !  Not  childish, 
but  fatuous  :  real  childishness  is  delightful.  I  knew  an  infant 
to  whom,  before  he  could  speak  plain,  his  parents  had  attempted 
to  give  notions  of  the  Divine  attributes :  a  wise  plan,  many  think. 
His  father  had  dandled  him  up-side-down,  ending  with,  There 
now  !  Papa  could  not  dance  on  his  head !  The  mannikin  made 
a  solemn  face,  and  said,  But  Dod  tood !  I  think  the  Doctor  has 


CHILDHOOD   AND   PRIESTHOOD  401 

rather  mistaken  the  way  of  becoming  as  a  little  child,  intended  in 

Matt,  xviii.  3  :  let  us  hope  the  will  may  be  taken  for  the  deed. 
Two  poets  have  given  images  of  transition  from  infancy  to 

manhood  :  Dryden, — for  the  Hind  is  Dryden  himself  on  all  fours; 

and  Wordsworth,  in  his  own  character  of  broad-nailed,  featherless 

biped  : — 

The  priest  continues  what  the  nurse  began, 
And  thus  the  child  imposes  on  the  man. 

The  child  's  the  father  of  the  man, 
And  I  could  wish  my  days  to  be 
Bound  each  to  each  by  natural  piety. 

In  Wordsworth's  aspiration  it  is  meant  that  sense  and  piety 
should  grow  together :  in  Dryden's  description  a  combination  of 
Mysticism  And  Bigotry  (can  this  be  the  double  Vahu  ?),  personi- 
fied as  '  the  priest,' — who  always  catches  it  on  this  score,  though 
the  same  spirit  is  found  in  all  associations, — succeeds  the  boguey- 
teaching  of  the  nurse.  Never  was  the  contrast  of  smile  and  scowl, 
of  light  and  darkness,  better  seen  than  in  the  two  pictures.  But 
an  acrostic  distinction  may  be  drawn.  When  mysticism  predomi- 
nates over  bigotry,  we  have  the  grotesque  picturesque,  and  the 
natural  order  of  words  gives  us  Mob,  an  appropriate  suggestion. 
But  when  bigotry  has  the  upper  hand,  we  see  Bam,  which  is  just 
as  appropriate ;  for  bigotry  nearly  always  deals  with  facte  and 
logic  so  as  to  require  the  application  of  at  least  one  of  the  minor 
wo.rds  by  which  dishonesty  is  signified.  I  think  that  M  is  the 
Doctor's  initial,  and  that  Queen  Mab  tickles  him  in  his  sleep  with 
the  sharp  end  of  a  6. 

(Monday,  August  21.)  Three  weeks  having  elapsed  without 
notice  from  me  of  the  Doctor,  I  receive  a  reminder  of  his  exist- 
ence, in  which  I  find  that  as  I  am  the  Daniel  who  judges  the 
Magi  of  Babylon,  it  is  to  be  pointed  out  that  Daniel  '  bore  a 
certain  number,  that  of  a  man  (beloved),  Daniel,  ch.  10.  v.  11, 
jind  which  you  certainly  do  not.'  Then,  '  by  Greek  power,' 
Belteshazzar  is  made  —  666.  Here  is  another  awkward  imita- 
tion of  the  way  of  a  baby  child.  When  you  have  sported  with 
the  tiny  creature  until  it  runs  away  offended,  by  the  time 
you  have  got  into  conversation  again  you  will  find  the  game  is 
to  be  renewed :  a  little  head  peeps  out  from  a  hiding-place  with 
'  I  don't  love  you.'  The  proper  rejoinder  is,  '  Very  well !  then  I  '11 
have  pussy.'  But  in  the  case  before  me  there  is  a  rule  of  three 
sum  to  do  ;  as  baby  '.  pussy  Dr.  ::  666  I  the  answer  required.  I 
will  work  it  out,  if  I  can. 

D  D 


402  A   BUDGET   OF  PARADOXES. 

The  squaring  of  the  circle  and  the  discovery  of  the  Beast  are 
the  two  goals — and  gaols  also — of  many  unbalanced  intellects, 
and  of  a  few  instances  of  a  better  kind.  I  might  have  said  more 
of  666,  but  I  am  not  deep  in  its  bibliography.  A  work  has  come 
into  my  hands  which  contains  a  large  number  of  noted  cases  :  to 
some  of  my  readers  it  will  be  a  treat  to  see  the  collection  ;  and 
the  sight  will  perhaps  be  of  some  use  to  those  who  have  read 
controversy  on  the  few  celebrated  cases  which  are  of  general 
notoriety.  It  is  written  by  a  learned  decipherer,  a  man  who 
really  knew  the  history  of  his  subject,  the  Eev.  David  Thorn,  of 
Bold  Street  Chapel,  Liverpool,  who  died,  I  am  told,  a  few  years  ago. 

Anybody  who  reads  his  book  will  be  inclined  to  parody  a  criti- 
cism which  was  once  made  on  Paley's  Evidences — '  Well  !  if  there 
be  anything  in  Christianity,  this  man  is  no  fool.'  And,  if  he  should 
chance  to  remember  it,  he  will  be  strongly  reminded  of  a  sentence 
in  my  opening  chapter, — '  The  manner  in  which  a  paradoxer  will 
show  himself,  as  to  sense  or  nonsense,  will  not  depend  upon  what 
he  maintains,  but  upon  whether  he  has  or  has  not  made  a  suffi- 
cient knowledge  of  what  has  been  done  by  others,  especially  as  to 
the  mode  of  doing  it,  a  preliminary  to  inventing  knowledge  for 
himself.'  And  this  is  reinforced  by  the  fact  that  Mr.  Thorn, 
though  a  scholar,  was  not  conspicuous  for  learning,  except  in  this 
his  great  pursuit.  He  was  a  paradoxer  on  other  points.  He 
reconciled  Calvinism  and  eternal  reprobation  with  Universalism 
and  final  salvation  ;  showing  these  two  doctrines  to  be  all  one. 

This  gentleman  must  not  be  confounded  with  the  Rev.  John 
Hamilton  Thorn  (no  relation),  at  or  near  the  same  time,  and 
until  recently,  of  Renshaw  Street  Chapel,  Liverpool,  who  was  one 
of  the  minority  in  the  Liverpool  controversy  when,  nearly  thirty 
years  ago,  three  heretical  Unitarian  schooners  exchanged  shotted 
sermons  with  thirteen  Orthodox  ships  of  the  line,  and  put  up 
their  challengers'  dander — an  American  corruption  of  d — d  anger 
— to  such  an  extent,  by  quiet  and  respectful  argument,  that  those 
opponents  actually  addressed  a  printed  intercession  to  the 
Almighty  for  the  Unitarian  triad,  as  for  '  Jews,  Turks,  Infidels, 
and  Heretics.'  So  much  for  the  distinction,  which  both  gentle- 
men would  thank  me  for  making  very  clear :  I  take  it  quite  for 
granted  that  a  guesser  at  666  would  feel  horrified  at  being  taken 
for  a  Unitarian,  and  that  a  Unitarian  would  feel  queerified  at 
being  taken  for  a  guesser  at  666.  Mr.  David  Thorn's  book  is 
'  The  Number  and  Names  of  the  Apocalyptic  Beasts,'  Part  I. 
1848,  8vo. :  I  think  the  second  part  was  never  published.  I  give 
the  Greek  and  Latin  solutions,  omitting  the  Hebrew:  as  usual, 
all  the  Greek  letters  are  numeral,  but  only  M  D  C  L  X  V  I  of  the 


NAMES   OF   THE  BEAST.  403 

Latin.  I  do  not  give  either  the  decipherers  or  their  reasons :  I 
have  not  room  for  this  ;  nor  would  I,  if  I  could,  bias  my  reader 
for  one  rather  than  another. 

D.  F.  Julianus  Coesar  Athens  (or  Aug.) ;  Diocles  Augustus  ; 
Ludovicus  ;  Silvester  Secundus  ;  Linus  Secundus ;  Vicarius  Filii 
Dei ;  Doctor  et  Eex  Latinus ;  Paulo  V.  Vice-Deo ;  Vicarius 
Greneralis  Dei  in  Terris  ;  Ipse  Catholicse  Ecclesiae  Visibile  Caput ; 
Dux  Cleri ;  Una,  Vera,  Catholica,  Infallibilis  Ecclesia ;  Auctoritas 
politica  ecclesiasticaque  Papalis  (Latina  will  also  do) ;  Lutherus 
Ductor  Grregis ;  Calvinus  tristis  fidei  interpres ;  Die  Lux ; 
Ludvvic ;  Will.  Laud;  Aarstvos;  77  Xarivr)  /SacnXeta;  £KK\r)aia 
eva:>$as  ;  rsirav,  apvovps  ;  Xa/ATreri?  ;  6  viKr)Trjs ;  KCLKOS 
a\T]Br}s  ftXaftepos ;  7ra\ai  {Barfcavos ;  d/tvo?  abucos  ; 
j-i'crrjptKov  ;  sviras ;  HsvsSi/cTos  ;  Boi/i/Sa^toy  7.  TraTra  £. 
t].  s.  s.  a.,  meaning  Boniface  III.  Pope  68th,  bishop  of  bishops  the 
first !  OV\TTIO<!  ;  Sios  slpi  77  rjpas ;  77  /ztcrtra  17  TrcnrtKr) ;  \ov9  pava  ; 
dvTtQios  (Beza) ;  17  d\a£ovsia  /Stow ;  Mao/u,fTis ; 
6sos  stfjii  eiri  yairjs  ;  laTTcTos ;  TraTrenr/coy ;  Sto/cXa- 
\acriavos  ;  %«tva  ;  ftpuaia  ;  loy  ITafi/e  ;  KOVTTOICS  (cowpox,  *  being 
the  vaw  ;  certainly  the  vaccinated  have  the  mark  of  the  Beast)  ; 
RoviSTrapTT) ;  N.  'Boi'r/Trapre  ;  evjropia;  Traoa&ocris ;  TO  fisya^tjpiov. 

All  sects  fasten  this  number  on  their  opponents.  It  is  found 
in  Martin  Lauter,  affirmed  to  be  the  true  way  of  writing  the 
name,  by  carrying  numbers  through  the  Eoman  Alphabet.  Some 
Jews,  according  to  Mr.  Thorn,  found  it  in  >n^J  IB"  Jesus  of 
Nazareth.  I  find  on  inquiry  that  this  satire  was  actually  put 
forth  by  some  mediaeval  rabbis,  but  that  it  is  not  idiomatic :  it 
represents  quite  fairly  '  Jesus  Nazarene,'  but  the  Hebrew  wants 
an  article  quite  as  much  as  the  English  wants  '  the.' 

Mr.  David  Thorn's  own  solution  hits  hard  at  all  sides :  he  finds 
a  666  for  both  beasts ;  77  <f>pijv  (the  mind)  for  the  first,  and 
J  (K\rj<Ttat,  crapvt.fa'.  (fleshly  churches)  for  the  second.  A  solution 
which  embodies  all  mental  philosophy  in  one  beast  and  all 
dogmatic  theology  in  the  other,  is  very  tempting :  for  in  these 
are  the  two  great  supports  of  Antichrist.  It  will  not,  however, 
mislead  me,  who  have  known  the  true  explanation  a  long  time. 
The  three  sixes  indicate  that  any  two  of  the  three  subdivisions, 
Iloman,  Greek,  and  Protestant,  are,  in  corruption  of  Christianity, 
six  of  one  and  half  a  dozen  of  the  other :  the  distinctions  of 
units,  tens,  hundreds,  are  nothing  but  the  old  way  (1  Samuel 
xviii.  7,  and  Concordance  at  ten,  hundred,  thousand)  of  symbol- 

differences  of  number  in  the  subdivisions. 
It  may  be  good  to  know  that,  even  in  speculations  on  666, 


404  A   BUDGET   OF  PARADOXES. 

there  are  different  degrees  of  unreason.  All  the  diviners,  when 
they  get  a  colleague  or  an  opponent,  at  once  proceed  to  reckon 
him  up  :  but  some  do  it  in  play  and  some  in  earnest.  Mr.  David 
Thorn  found  a  young  gentleman  of  the  name  of  St.  Claire  busy 
at  the  Beast  number :  he  forthwith  added  the  letters  in  or  rcXaipe 
and  found  666  :  this  was  good  fun.  But  my  spiritual  tutelary, 
when  he  found  that  he  could  not  make  a  beast  of  me,  except  by 
changing  N  into  H,  solemnly  referred  the  difficulty  to  the  Al- 
mighty :  this  was  poor  earnest. 

I  am  glad  I  did  not  notice,  in  time  to  insert  it  in  the 
Athenceum,  a  very  remarkable  paradoxer  brought  forward  by 
Mr.  Thorn,  his  friend  Mr.  Wapshare :  it  is  a  little  too  strong  for 
the  general  public.  In  the  Athenceum  they  would  have  seen  and 
read  it :  but  this  book  will  be  avoided  by  the  weaker  brethren. 
It  is  as  follows  : — 

'  God,  the  Elohim,  was  six  days  in  creating  all  things,  and  having 
made  MAN,  he  entered  into  his  rest.  He  is  no  more  seen  as  a  Creator, 
as  Elohim,  but  as  Jehovah,  the  Lord  of  the  Sabbath,  and  the  Spirit  of 
life  in  MAN,  which  Spirit  worketh  sin  in  the  flesh ;  for  the  Spirit  of 
Love,  in  all  flesh,  is  Lust,  or  the  spirit  of  a  beast,  So  Bom.  vii.  And 
which  Spirit  is  crucified  in  the  flesh.  He  then,  as  Jehovah — as  the 
power  of  the  Law,  in  and  over  all  flesh,  John  viii.  44 — increases  that 
which  he  has  made  as  the  Elohim,  and  his  power  shall  last  for  6  days, 
or  6  periods  of  time,  computed  at  a  millennium  of  years  ;  and  at  the  end 
of  which  six  days,  he  who  is  the  Spirit  of  all  flesh  shall  manifest  him- 
self as  the  Holy  Spirit  of  Almighty  Love,  and  of  all  truth  ;  and  so  shall 
the  Church  have  her  Sabbath  of  Rest — all  contention  being  at  an  end. 
This  is,  as  well  as  I  may  now  express  it,  my  solution  of  the  mystery  in 
Hebrew,  and  in  Greek,  and  also  in  Latin,  I H  S.  For  he  that  was 
lifted  up  is  King  of  the  Jews,  and  is  the  Lord  of  all  Life,  working  in 
us,  both  to  will  and  to  do  ;  as  is  manifest  in  the  Jews — they  slaying 
htm  that  his  blood  might  be  good  for  the  healing  of  the  nations,  .of  all 
people  and  tongues.  As  the  Father  of  all  natural  flesh,  he  is  the  Spirit 
of  Lust,  as  in  all  beasts  ;  as  the  Father,  or  King  of  the  Jews,  he  is  the 
Devil,  as  he  himself  witnesseth  in  John  viii.,  already  referred  to.  As 
lifted  up,  he  is  transformed  into  the  Spirit  of  Love,  a  light  to  the 
Gentiles,  and  the  glory  of  his  people  Israel  .  .  .  For  there  is  but  o.N7  E 
God,  ONE  Lord,  ONE  Spirit,  ONE  body,  &c.  and  he  who  was  Satan,  the 
Spirit  of  life  in  that  body,  is,  in  Christ  crucified,  seen  in  the  Spirit 
that  is  in  all,  and  through  all,  and  over  all,  God  blessed  for  ever.' 

All  this  seems  well  meant,  and  Mr.  Thorn  prints  it  as  convinced 
of  its  piety,  and  '  pronounces  no  opinion.'  Mystics  of  all  sorts ! 
see  what  you  may  come  to,  or  what  may  come  to  you  !  I  have 
inserted  the  above  for  your  good. 

There  is  nothing  in  this  world  so  steady  as  some  of  the  para- 
doxers.  They  are  like  the  spiders  who  go  on  spinning  after  they 


IN   RE  ,^-J.  405 

have  web  enough  to  catch  all  the  flies  in  the  neighbourhood,  if 
the  flies  would  but  come.  They  are  like  the  wild*  bees  who  go  on 
making  honey  which  they  never  can  eat,  proving  sic  vos  non 
vobis  to  be  a  physical  necessity  of  their  own  contriving.  But 
nobody  robs  their  hives:  no,  unlike  the  bees,  they  go  about 
offering  their  ware  to  any  who  will  take  it  at  a  gift.  I  had  just 
written  the  last  sentence  (Oct.  30,  1866,  8'45  A.M.)  when  in  comes 
the  second  note  received  this  morning  from  Dr.  Thorn:  at  1'30 
P.M.  came  in  a  third.  These  arise  out  of  the  above  account  of  the 
Rev.  D.  Thorn,  published  Oct.  27  :  three  notes  had  arrived  before. 
For  curiosity  I  give  one  day's  allowance,  supposing  these  to  be 
all  :  more  may  arrive  before  night. 

29th  Oct.  1866. 

Dear  Sir, — 

In  re  pl_i. 

So  that  '  Zaphnath  Paaneah  '  may  be  after  all  the  revealer  of  the 
Northern  Tau,'  Qarepob) — To  make  manifest,  shew,  or  explain;  and 
this  may  satisfy  the  House  of  Joseph  in  Amos  5C.  While  Belteshazzar 
=666  may  be  also  satisfactory  to  the  House  of  David,  and  so  we  may 
have  Zech.  10°.  6V.  in  operation  when  Ezekiel  37C.  16V.  has  been 
realised  ; — but  there,  what  is  the  use  of  writing,  it  is  al  Coptic  to  a 

man  who  has  not  r-j^,  The  Thau  of  the  North,  the  double  Vahu  11. 
Look  at  Jeremiah  3C.  8V.  and  then  to  Psalm  83  for  '  hidden  ones ' 
niiT1  *J-1QV — The  Zephoni  Jehovah,  and  say  whether  they  have  any 
connection  with  the  Zephon  Thau.  The  Hammer  of  Thor  of 
Jeremiah  23C.  29V.  as  I  gave  you.  in  No.  3  of  my  present  edition. 

Yours  truly 

LE  CHEVALIER  AU  CIN. 

By  Greek  Power. 

C  =     20 

n  =       8 

E  =       5 

v  =       6 

A  =       1 

L  =     30 

i  =     10  There  will  be  thousands  of  Morgans 

E  =       5  who    will    be    among    the    wise   and 

B  =100  prudent  of  Hosea  14°.   9T.    when  the 

Seventh  Angel  sounds,  let  me  number 

A  =        1  that  One  by  Greek,  Rev.  17C.  lv  :— 

u  =  400 

C    =     20 
i      =     10 

N     =     50 

666 


4-0 G  A   BUDGET   OF  PARADOXES. 


s  = 

200 

E       = 

5 

XV       = 

6 

E       = 

5 

N       = 

50 

T       = 

300 

H       = 

8 

A.    = 

1 

N       = 

50 

X    Q       = 

6 

L       ^^ 

30 

666 

to 

2 
o 


g 
o    co 


London,  October  29,  1866. 
Dear  Sir, — 

In  re  r-^T1  versus  »J<. 

However  pretentious  the  X  or  >J<  may  be,  and  it  is  peculiarly  so 
just  now  in  this  land ;  after  all  it  is  only  made  of  two  Roman  Vs — 
and  so  is  only  =  )(  (10) — and  therefore  is  not  the  perfect  number  12 
of  Reveln,  but  is  the  mark  of  the  goddess  Decima  \ 

Yours  truly 

WM.  THOEN. 


Had  the  one  who  sent  forth  a  pastoral  (Romish)  the  other  day, 
remained  amongst  the  faithful  expectants,  see  how  he  would  have 
numbered,  whereas  he  sold  himself  for  the  privilege  of  signing 

>J<  HENRY  E.  MANNING. 

Shilling  versus  Franc. 

Teutonic  Long  Hundred  120  versus  100  or  the  Decimal  question. 


MR,   GLADSTONE  666.  407 


By  English  Key. 

H  =         8 

E  =         5 

N  =  40 

.  =  80  §    §• 

Y     =    14° 


M 


.    T 


a   8  g 
*   >•  •— i 


E     = 

5 

D      = 

4 

w     = 

120 

A        = 

1 

E        = 

80 

D        = 

4 

M    = 

30 

A        = 

1 

N      = 

40 

N       = 

40 

I        = 

9 

N       = 

40 

G       = 

7 

+  = 

12 

666 


Cutting  from  newspaper  : — 

ITALY. 

Rome  (vid  Marseilles),  October  24. 
Mr.  Gladstone  has  paid  a  visit  to  the  Pope. 

By  Greek  Power. 


G 

= 

6 

L 

:= 

30 

A 

= 

1 

D 

= 

4 

S 

— 

200 

T 

= 

300 

0 

= 

70 

N 

= 

50 

E 

= 

5 

666 
And  what  then  +  ? 


408  A   BUDGET   OF  PARADOXES. 

In  other  letters  John  Stuart  Mill  is  666  if  the  a  be  left  out ; 
Chasuble  is  perfect.  John  Brighte  is  a  fait  accompli  ;  and  I  am 
asked  whether  intellect  can  account  for  the  final  e.  Very  easily  : 
this  Beast  is  not  the  M.  P.,  but  another  person  who  spells  his 
name  differently.  But  if  John  Sturt  Mill  and  John  Brighte 
choose  so  to  write  themselves,  they  may. 

A  curious  collection ;  a  mystical  phantasmagoria !  There  are 
those  who  will  try  to  find  meaning :  there  are  those  who  will  try 
to  find  purpose. 

And  some  they  said — What  are  you  at  ? 
And  some — What  are  you  arter  ? 

My  account  of  Mr.  Thorn  and  his  666  appeared  on  October  27  : 
and  on  the  29th  I  received  from  the  editor  a  copy  of  Mr.  Thorn's 
sermons  .published  in  1863  (he  died  Feb.  27,  1862)  with  best 
wishes  for  iny  health  and  happiness.  The  editor  does  not  name 
himself  in  the  book  ;  but  he  signed  his  name  in  my  copy :  and 
may  my  circumference  never  be  more  than  3£  of  my  diameter  if 
the  signature,  name  and  writing  both,  were  not  that  of  my 
0  Ding  friend  Mr.  James  Smith  !  And  so  I  have  come  in  contact 
with  him  on  666  as  well  as  on  TT  !  I  should  have  nothing  left  to 
live  for,  had  I  not  happened  to  hear  that  he  has  a  perpetual 
motion  on  hand.  I  returned  thanks  and  kind  regards :  and 
Miss  Miggs's  words — '  Here's  forgivenesses  of  injuries !  here's 
amicablenesses ! ' — rang  in  my  ears.  But  I  was  made  slightly 
uncomfortable :  how  could  the  war  go  on  after  this  armistice  ? 
Could  I  ever  make  it  understood  that  the  truce  only  extended  to 
the  double  Vahu  and  things  thereunto  relating  ?  It  was  once 
held  by  seafaring  men  that  there  was  no  peace  with  Spaniards 
beyond  the  line :  I  was  determined  that  there  must  be  no  concord 
with  J.  S.  inside  the  circle;  that  this  must  be  a  special  exception, 
like  Father  Huddleston  and  old  Grouse  in  the  gun-room.  I  was 
not  long  in  anxiety ;  twenty-four  hours  after  the  book  of  sermons 
there  came  a  copy  of  the  threatened  exposure — '  The  British 
Association  in  Jeopardy,  and  Professor  De  Morgan  in  the  Pillory 
without  hope  of  escape.  By  James  Smith,  Esq.'  London  and 
Liverpool,  8vo.,  1866  (pp.  94).  This  exposure  consists  of 
reprints  from  the  Athenceum  and  Correspondent :  of  things  new 
there  is  but  one.  In  a  short  preface  Mr.  J.  S.  particularly  recom- 
mends to  '  read  to  the  end'  At  the  end  is  an  appendix  of  two 
pages,  in  type  as  large  as  the  work  ;  a  very  prominent  peroration. 
It  is  an  article  from  the  Athenceum,  left  out  of  its  place.  In  the 
last  sentence  Mr.  J.  Smith,  who  had  asked  whether  his  character 


J.  S.'S   SYMBOLICAL   REASONING. 

as  an  honest  Geometer  and  Mathematician  was  not  at  stake,  is 
warned  against  the  fallacia  plarium  interroyafionum.  He  is 
told  that  there  is  not  a  more  honest  what's-his-name  in  the 
world :  but  that  as  to  the  counter  which  he  calls  his  character  as 
a  mathematician,  he  is  assured  that  it  had  been  staked  years  ago, 
and  lost.  And  thus  truth  has  the  last  word.  There  is  no  occa- 
sion to  say  much  about  reprints.  One  of  them  is  a  letter  [that 
given  above]  of  August  25,  1865,  written  by  Mr.  J.  S.  to  the 
Correspondent.  It  is  one  of  his  quadratures ;  and  the  joke  is 
that  I  am  made  to  be  the  writer :  it  appears  as  what  Mr.  J.  S. 
hopes  I  shall  have  the  sense  to  write  in  the  Athenceum  and  fore- 
stall him.  When  I  saw  myself  thus  quoted — yes !  quoted  ! 
double  commas,  first  person — I  felt  as  I  suppose  did  \Vm.  Wilber- 
force  when  he  set  eyes  on  the  affectionate  benediction  of  the 
potato  which  waggish  comrades  had  imposed  on  a  raw  Irish 
reporter  as  part  of  his  speech.  I  felt  as  Martin  of  Galvvay — kind 
friend  of  the  poor  dumb  creatures ! — when  he  was  told  that 
the  newspapers  had  put  him  in  Italics.  '  I  appeal  to  you, 
Mr.  Speaker !  I  appeal  to  the  House !  Did  I  speak  in  Italics  ? 
Do  I  ever  speak  in  Italics  ? '  I  appeal  to  editor  and  readers, 
whether  I  ever  squared  the  circle  until  a  week  or  two  ago,  when 
I  gave  my  charitable  mode  of  reconciling  the  discrepant  cyclo- 
meters. 

The  absurdity  of  the  imitation  of  symbolic  reasoning  is  so 
lusciously  rich,  that  I  shall  insert  it  when  I  make  up  my  final 
book.  Somebody  mastered  Spanish  merely  to  read  Don  Quixote : 
it  would  be  worth  while  to  learn  a  little  algebra  merely  to  enjoy 
this  a  6-istical  attack  on  the  windmills.  The  principle  is,  Prove 
something  in  as  roundabout  a  way  as  possible,  mention  the  circle 
once  or  twice  irrelevantly  in  the  course  of  your  proof,  and  then 
make  an  act  of  Q.  E.  D.  in  words  at  length.  The  following  is 
hardly  caricature : — 

To  prove  that  2  and  2  make  5.  Let  a  =  2,  b  =  5  :  let  c  = 
658,  the  number  of  the  House  :  let  d  =  666,  the  number  of  the 
Beast.  Then  of  necessity  d  =  a  +  b  +  c  +  1  ;  so  that  1  is  a 
harmonious  and  logical  quantification  of  the  number  of  which  we 
are  to  take  care.  Now,  6,  the  middle  of  our  digital  system,  is, 
by  mathematical  and  geometrical  combination,  a  mean  between 
5+1  and  2  +  2.  Let  1  be  removed  to  be  taken  care  of,  a 
thing  no  real  mathematician  can  refuse  without  serious  injury 
to  his  mathematical  and  geometrical  reputation.  It  follows  of 
necessity  that  2+2  =  5,  quod  erat  demonstvumhorrendum. 
If  Simpkin  &  Marshall  have  not,  after  my  notice,  to  account  for 


410  A   BUDGET   OF   PARADOXES. 

a  gross  of  copies  more  than  would  have  gone  off  without  me,  the 
world  is  not  worthy  of  its  James  Smith  ! 

The  only  fault  of  the  above  is,  that  there  is  more  connexion 
than  in  the  process  of  Faber  Cyclometricus  :  so  much,  in  fact, 
that  the  blunders  are  visible.  The  utter  irrelevance  of  premises 
to  conclusion  cannot  be  exhibited  with  the  requisite  obscurity  by 
any  one  who  is  able  to  follow  reasoning :  it  is  high  art  displayed 
in  a  certain  toning  down  of  the  cegri  somnia,  which  brings  them 
to  a  certain  look  of  approach  to  reasoning  which  I  can  only 
burlesque.  Mr.  J.  S.  produces  something  which  resembles  argu- 
ment much  as  a  chimpanzee  in  dolour,  because  balked  of  his 
dinner,  resembles  a  thinking  man  at  his  studies.  My  humble 
attempt  at  imitation  of  him  is  more  like  a  monkey  hanging  by 
his  tail  from  a  tree  and  trying  to  crack  a  cocoa-nut  by  his 
chatter. 

I  could  forgive  Mr.  J.  S.  anything,  properly  headed.  I  would 
allow  him  to  prove — for  himself — that  the  Quadrature  of  the 
Circle  is  the  child  of  a  private  marriage  between  the  Bull  Uni- 
genitus  and  the  Pragmatic  Sanction,  claiming  tithe  of  onions  for 
repeal  of  the  Mortmain  Act,  before  the  Bishops  in  Committee 
under  the  kitchen  table :  his  mode  of  imitating  reason  would  do 
this  with  ease.  But  when  he  puts  his  imitation  into  my  mouth, 
to  make  me  what  he  calls  a  '  real  mathematician,'  my  soul  rises 
in  epigram  against  him.  I  say  with  the  doll's  dressmaker — such 
a  job  makes  me  feel  like  a  puppet's  tailor  myself — '  He  ought  to 
have  a  little  pepper  ?  just  a  few  grains  ?  I  think  the  young  man's 
tricks  and  manners  make  a.  claim  upon  his  friends  for  a  little 
pepper?'  De  Faure  and  Joseph  Scaliger  come  into  my  head: 
my  reader  may  look  back  for  them. 

Three  circlesquarers  to  the  manner  born, 
Switzerland,  France,  and  England  did  adorn, 
De  Faure  in  equations  did  surpass,  (p.  89) 
Joseph  at  contradictions  was  an  ass.  (p.  67) 
Groaned  Folly,  I'm  used  up  !   What  shall  I  do 
To  make  James  Smith  ?  Grinned  Momus,  Join  the  two  ! 
As  to  my  locus  poenitenticv,  the  reader  who  is  fit  to  enjoy  the 
letter  I  have  already  alluded  to  will  see  that  I  have  a  soft  and 
easy  position  ;  that  the  thing  is  really  a  piUowry ;  and  that  I 
am,  like  Perrette's  pot  of  milk, 

Bien  pose  sur  un  coussinet. 

Joanna  Southcott  never  had  a  follower  who  believed  in  her  with 
more  humble  piety  than  Mr.  James  Smith  believes  in  himself. 
After  all  that  has  happened  to  him,  he  asks  me  with  high  confidence 


A   SCHOOLBOY'S   DEFENCE.  411 

to  '  favour  the  writer  with  a  proof  that  I  still  continue  of  opinion 
that  '  the  best  of  the  argument  is  in  my  jokes,  and  the  best  of 
the  joke  is  in  his  arguments.'  I  will  not  so  favour  him.  At  the 
very  outset  I  told  him  in  plain  English  that  he  has  the  whiphand 
of  all  the  reasoners  in  the  world,  and  in  plain  French  that  il  a 
perdu,  le  droit  d'etre  frappe  de  ^evidence ;  I  might  have  said 
pendu.  To  which  I  now  add,  in  plain  Latin,  Sapienti  pauca, 
indocto  nihil.  The  law  of  Chancery  says  that  he  who  will  have 
equity  must  do  equity :  the  law  of  reasoning  says  that  he  who 
will  have  proof  must  see  proof. 

The  introduction  of  things  quite  irrelevant,  by  way  of  reproach, 
is  an  argument  in  universal  request :  and  it  often  happens  that 
the  argument  so  produced  really  tells  against  the  producer.  So 
common  is  it  that  we  forget  how  boyish  it  is ;  but  we  are 
strikingly  reminded  when  it  actually  comes  from  a  boy.  In  a 
certain  police  court,  certain  small  boys  were  arraigned  for  con- 
spiring to  hoot  an  obnoxious  individual  on  his  way  from  one  of 
their  school  exhibitions.  This  proceeding  was  necessary,  because 
there  seemed  to  be  a  permanent  conspiracy  to  annoy  the  gentle- 
man ;  and  the  masters  did  not  feel  able  to  interfere  in  what  took 
place  outside  the  school.  So  the  boys  were  arraigned  ;  and  their 
friends,  as  silly  in  their  way  as  themselves,  allowed  one  of  them 
to  make  the  defence,  instead  of  employing  counsel ;  and  did  not 
even  give  them  any  useful  hints.  The  defence  was  as  follows ; 
and  any  one  who  does  not  see  how  richly  it  sets  off  the  defences 
of  bigger  boys  in  bigger  matters  has  much  to  learn.  The  inno- 
cent conviction  that  there  was  answer  in  the  latter  part  is 
delightful.  Of  course  fine  and  recognizance  followed. 

A said  the  boys  had  received  great  provocation  from  B . 

He  was  constantly  threatening  them  with  a  horsewhip  which  he 
carried  in  his  hand  [the  boy  did  not  say  what  had  passed  to  induce 
him  to  take  such  a  weapon],  and  he  had  repeatedly  insulted 

the  master,  which  the  boys  could  not  stand.  B had  in  his 

own  drawing-room  told  him  (A )  that  he  had  drawn  his 

sword  against  the  master  and  thrown  away  the  scabbard.  B . 

knew  well  that  if  he  came  to  the  college  he  would  catch  it,  an4 
then  he  went  off  through  a  side  door — which  was  no  sign  of 

pluck  ;  and  then  he  brought  Mrs.  B with  him,  thinking  that 

her  presence  would  protect  him. 

My  readers  may  expect  a  word  on  Mr.  Thorn's  sermons,  after 
my  account  of  his  queer  doings  about  666.  He  is  evidently  an 
honest  and  devout  man,  much  wanting  in  discrimination.  He 
has  a  sermon  about  private  judgment,  in  which  he  halts  between 


412  A   BUDGET   OF  PAKADOXES. 

the  logical  and  legal  meanings  of  the  word.  He  loathes  those 
who  apply  their  private  judgment  to  the  word  of  Grod :  here  he 
means  those  who  decide  what  it  ought  to  be.  He  seems  in  other 
places  aware  that  the  theological  phrase  means  taking  right  to 
determine  what  it  is.  He  uses  his  own  private  judgment  very 
freely,  and  is  strong  in  the  conclusion  that  others  ought  not 
to  use  theirs  except  as  he  tells  them  how  ;  he  leaves  all  the  rest 
of  mankind  free  to  think  with  him.  In  this  he  is  not  original : 
his  fame  must  rest  on  his  senary  tripod. 

Mr.  James  Smith's  procedures  are  not  caricature  of  reasoning  ; 
they  are  caricature  of  blundering.  The  old  way  of  proving  that 
2  =  1  is  solemn  earnest  compared  with  his  demonstrations.  As 
follows : 

Let  x  =  1 

Then         x2  =  x 

And  «2  —  1  =  x  —  1 

Divide  both  sides  by  x  —  1  ;  then 

x  +  \  =  I  ;  but  x  =  1,  whence  2=1 

When  a  man  is  regularly  snubbed,  bullied,  blown  up,  walked 
into,  and  put  down,  there  is  usually  some  reaction  in  his  favour, 
a  kind  of  deostracism,  which  cannot  bear  to  hear  him  always 
called  the  blunderer.  I  hope  it  will  be  so  in  this  case.  There 
is  nothing  I  more  desire  than  to  see  sects  of  paradoxers.  There 
are  fully  five  thousand  adults  in  England  who  ought  to  be  the 
followers  of  some  one  false  quadrature.  And  I  have  most  hope 
of  3£,  because  I  think  Mr.  James  Smith  better  fitted  to  be  the 
leader  of  an  organised  infatuation  than  any  one  I  know  of.  He 
wants  no  pity,  and  will  get  none.  He  has  energy,  means,  good 
humour,  strong  conviction,  character,  and  popularity  in  his  own 
circle.  And,  most  indispensable  point  of  all,  he  sticks  at  nothing ; 
In  ccelum  jusseris,  ibit. 

When  my  instructor  found  I  did  not  print  an  acceptance  of  what 
I  have  quoted,  he  addressed  me  as  follows  (Corr.,  Sept.  23): — 

'  In  this  life,  however,  we  must  do  our  duty,  and,  when  necessary,  use 
the  rod,  not  in  a  spirit  of  revenge,  but  for  the  benefit  of  the  culprit 
and  the  good  of  society.  Now,  Sir,  the  opportunity  has  been  thrown 
in  your  way  of  slipping  out  of  the  pillory  without  risk  of  serious  in- 
jury ;  but,  like  an  obstinate  urchin,  you  have  chosen  to  quarrel  with, 
your  opportunity  and  remain  there,  and  thus  you  compel  me  to  deal 
with  you  as  schoolmasters  used  to  do  with  stupid  boys  in  bygone  days 
— that  is  to  say,  you  force  me  to  the  use  of  the  critic's  rod,  compel  me 
to  put  you  where  little  Jack  Horner  sat,  and,  as  a  warning  to  other 
naughty  boys,  to  ornament  you  with  a  dunce's  cap.  The  task  I  set 


LITTLE   JACK  HORNER   AND   OTHERS.  413 

you  was  a  very  simple  one,  as  I  shall  make  manifest  at  the  proper 
time.' 

In  one  or  more  other  places,  as  well  as  this,  Mr.  Smith  shows 
that  he  does  not'know  the  legend  of  little  Jack  Homer,  whom  he 
imagines  to  be  put  in  the  corner  as  a  bad  boy.  This  is  curious  ; 
for  there  had  been  many  allusions  to  the  story  in  the  journal  he 
was  writing  in,  and  the  Christmas  pie  had  become  altered  into 
the  Seaforth  TT. 

Mr.  Smith  is  satisfied  at  last  that — what  between  argument  and 
punishment  he  has  convinced  me.  He  says  (Corr.,  Jan.  27,  1866) 
'  I  tell  him  without  hesitation  that  he  knows  the  true  ratio  of 
diameter  to  circumference  as  well  as  I  do,  and  if  he  be  wise  he 
will  admit  it.'  I  should  hope  I  do,  and  better ;  but  there  is  no 
occasion  to  admit  what  everybody  knows. 

I  have  often  wished  that  we  could  have  a  slight  glimpse  of  the 
reception  which  was  given  to  some  of  the  old  cyclometers:  but 
we  have  nothing,  except  the  grave  disapprobation  of  historians. 
I  am  resolved  to  give  the  New  Zealander  a  chance  of  knowing  a 
little  more  than  this  about  one  of  them  at  least ;  and,  by  the 
fortunate  entrance  into  life  of  the  Correspondent,  I  am  able  to  do 
it.  I  omit  sober  mathematical  answers,  of  which  there  were 
several.  The  following  letter  is  grave  earnest : — 

'  Sir, — I  have  watched  Mr.  James  Smith's  writings  on  this  subject 
from  the  first,  and  I  did  hope  that,  as  the  more  he  departs  from  truth 
the  more  easy  it  must  be  to  refute  him,  [this  by  no  means  always  true] 
some  of  your  correspondents  would  by  this  time  have  done  so.  I  own 
that  I  am  unable  to  detect  the  fallacy  of  his  argument ;  and  I  am 
quite  certain  that  '  II  '  is  wrong,  in  No.  23,  where  he  declares  that 
Mr.  Smith  is  '  ignorant  of  the  very  elements  of  mathematical  truth.' 
I  have  observed  an  immense  amount  of  geometrical  reasoning  on  his 
part,  and  I  cannot  see  that  it  is  either  fair  or  honest  to  deny  this, 
which  may  be  regarded  as  the  '  elements '  of  mathematical  truth. 
Would  it  not  be  better  for  '  II '  to  answer  Mr.  Smith,  to  refute  liis 
arguments,  to  point  out  their  fallacies,  and  to  save  learners  from  error, 
than  to  plunge  into  gross  insult  and  unmanly  abuse  ?  Would  it  not  be 
well,  also,  that  Professor  De  Morgan  should  favour  us  with  a  little 
reasoning  ? 

I  have  hitherto  seen  no  attempt  to  overthrow  Mr.  Smith's  argu- 
ments ;  I  trust  that  this  will  not  continue,  since  the  subject  is  one  of 
immense  importance  to  science  in  general,  especially  to  nautical 
science,  and  all  that  thereto  belongs.  Yours,  &c., 

A  CAPTAIN,  R.N.' 

On  looking  at  this  homoeopathic  treatment  of  the  3£  quadra- 
ture— remember,  homoeopathic,  similia  similibus,  not  infinite- 


414  A   BUDGET   OF  PARADOXES. 

simal — and  at  the  imputation  thrown  upon  it,  I  asked  myself, 
what  is  vulgarity  ?  No  two  agree,  except  in  this,  that  every  one 
"sees  vulgarity  in  what  is  directed  against  himself.  Mark  the 
world,  and  see  if  anything  be  so  common  as  the  description  of  the 
other  side's  remarks  as  '  vulgar  attempt  at  wit.'  '  I  suppose  you 
think  that  very  witty:'  the  answer  is  'No  my  friend!  your 
remark  shows  that  you  feel  it  as  wit,  so  that  the  purpose  is 
answered ;  I  keep  my  razor  for  something  else  than  cutting 
blocks ; '  I  am  inclined  to  think  that  '  out  of  place '  is  a  necessary 
attribute  of  true  vulgarity.  And  further,  it  is  to  be  noticed  that 
nothing  is  unproducible — salvo  pudore — which  has  classical 
authority,  modern  or  ancient,  in  its  favour,  'He  is  a  vulgar 
fellow ;  I  asked  him  what  he  was  upon,  and  what  do  you  think  he 
answered,  My  legs!' — 'Well,  and  has  he  not  justification  ?  what 
do  you  find  in  Terence  ?  Quid  agitur  ?  Statur.'  I  do  not  even 
blench  from  my  principle  where  I  find  that  it  brings  what  is 
called  '  taking  a  sight '  within  permissible  forms  of  expression : 
Rabelais  not  only  establishes  its  antiquity,  but  makes  it  English. 
Our  old  translation  }  has  it  thus  (book  2,  ch.  19) : — 

'  Then  made  the  Englishman  this  sign.  His  left  hand,  all  open, 
he  lifted  up  into  the  air,  then  instantly  shut  into  his  fist  the  four 
fingers  thereof;  and  his  thumb  extended  at  length  he  placed 
upon  the  tip  of  his  nose.  Presently  after  he  lifted  up  his  right 
hand  all  open  and  abased  and  bent  it  downwards,  putting  the 
thumb  thereof  in  the  very  place  where  the  little  finger  of  the  left 
hand  did  close  in  the  fist,  and  the  four  right  hand  fingers  he 
softly  moved  in  the  air.  Then  contrarily  he  did  with  the  right 
hand  what  he  had  done  with  the  left,  and  with  the  left  what  he 
had  done  with  the  right.' 

An  impressive  sight !  The  making  a  fist  of  the  left  hand  is  a 
great  addition  of  power,  and  should  be  followed  in  modern  prac- 
tice. The  gentle  sullation  of  the  front  fingers,  with  the  clenched 
fist  behind  them,  says  as  plainly  as  possible,  Put  suaviter  in  modo 
in  the  van,  but  don't  forget  to  have  fortiter  in  re  in  the  rear. 

My  Budget  was  announced  (March  23, 1867)  for  completion  on 
the  30th.  Mr.  James  Smith  wrote  five  letters,  one  before  the 
completion,  four  after  it ;  the  five  contained  68  pages  of  quarto 

1  Lors  feist  1'Anglois  tel  signe.  La  main  gausche  toute  ouverte  il  leva  hault  en 
1'aer,  puis  ferma  au  poing  les  quatres  doigtz  d'icelle  «t  le  poulce  estendu  assit  sus  la 
pinne  du  nez.  Soubdain  apres  leva  la  dextre  toute  ouverte,  et  toute  ouverte  la  baissa, 
joignant  la  poulce  au  lieu  que  fermait  le  petit  doigt  de  la  gausche,  et  les  quatre 
doigtz  d'icelle  mouvoit  lentement  en  1'aer.  Puis  au  rebours  feit  de  la  dextre  ce  qu'il 
avoit  faict  de  la  gausche,  et  de  la  gausche  ce  que  avoit  faict  de  la  dextre. 


DR    WHEWELL'S  LETTEE.  415 

letter  paper.  Mr.  J.  S.  had  picked  up  a  clerical  correspondent, 
with  whom  he  was  in  the  heat  of  battle. — 

March  27. — Dear  Sir.  Very  truly  yours.  Duty ;  for  my  own 
sake  ;  just  time  left  to  retrieve  my  errors ;  sends  copy  of  letter  to 
clergyman;  new  proof  never  before  thought  of;  merest  tyro  would 
laugh  if  I  were  to  stifle  it,  whether  by  rhodomontade  or  silent  con- 
tempt ;  keep  your  temper.  I  shall  be  convinced  ;  and  if  world  be 
right  in  supposing  me  incapable  of  a  foul  act,  I  shall  proclaim  glorious 
discovery  in  the  Athenaeum. 

April  15. Sir,  .  .  .  My  dear  Sir,  Your  sincere  tutelary.  Copy  of 

another  letter  to  clergyman  ;  discovery  tested  by  logarithms  ;  reasons 
such  as  none  but  a  knave  or  a  sinner  can  resist.  Let  me  advise  you  to 
take  counsel  before  it  is  too  late  !  Keep  your  temper.  Let  not  your  -pride 
get  the  better  of  your  discretion  !  Screw  up  your  courage,  my  good 
friend  and  resolve  to  show  the  world  that  you  are  an  honest  man  .  .  . 

April  20. — Sir  .  .  .  Your  very  sincere  and  favourite  tutelary.  I 
have  long  played  the  cur,  snapping  and  snarling  .  .  .  ;  suddenly  lost 
my  power,  and  become  half-starved  dog  without  spirit  to  bark  ;  try  if 
air  cannot  restore  me ;  calls  himself  the  thistle  in  allusion  to  my  other 
tutelary,  the  thorn ;  Would  I  prefer  his  next  work  to  be,  '  A  whip  for 
the  Mathematical  Cur,  Prof.  De  M.'  In  some  previous  letter,  which  I 
have  mislaid,  he  told  me  his  next  would  be  '  a  muzzle  for  the  Mathe- 
matical Bull  dog,  Prof.  De  M.' 

April  23. — Sir.  Very  sincerely  yours.  More  letters  to  clergyman  ; 
you  may  as  well  knock  your  head  against  a  stone  wall  to  improve  your 
intellect  as  attempt  to  controvert  my  proofs.  [I  thought  so  too  ;  and 
tried  neither]. 

May  6. — My  dear  Sir.     Very  sincerely  yours.     All  to  myself,  and 

nothing  to  note. 

july  2. No  more  in  this  interval.     All  that  precedes  is  a  desperate 

attempt  to  induce  me  to  continue  my  descriptions :  notoriety  at  any  price. 

I  dare  say  the  matter  is  finished  :  the  record  of  so  marked  an 
instance  of  self-delusion  will  be  useful. 

I  append  to  the  foregoing  a  letter  from  Dr.  Whewell  to  Mr. 
James  Smith.  The  Master  of  Trinity  was  conspicuous  as  a  rough 
customer,  an  intellectual  bully,  an  overbearing  disputant :  the 
character  was  as  well  established  as  that  of  Sam  Johnson.  But 
there  was  a  marked  difference.  It  was  said  of  Johnson  that  if 
his  pistol  missed  fire,  he  would  knock  you  down  with  the  butt 
end  of  it :  but  Whewell,  in  like  case,  always  acknowledged  the 
miss,  and  loaded  again  or  not,  as  the  case  might  be.  He  re- 
minded me  of  Dennis  Brulgruddery,  who  says  to  Dan,  Pacify  me 
with  a  good  reason,  and  you'll  find  me  a  dutiful  master.  I  knew 
him  from  the  time  when  he  was  my  teacher  at  Cambridge,  more 
than  forty  years.  As  a  teacher,  he  was  anything  but  dictatorial, 


416  A   BUDGET   OF  PARADOXES. 

and  he  was  perfectly  accessible  to  proposal  of  objections.  He 
came  in  contact  with  me  in  his  slashing  way  twice  in  our  after 
joint  lives,  and  on  both  occasions  he  acknowledged  himself  over- 
come, by  that  change  of  manner,  and  apologetic  mode  of  continu- 
ance, which  I  had  seen  him  employ  towards  others  under  like 
circumstances. 

I  had  expressed  my  wish  to  have  a  thermometer  of  probability, 
with  impossibility  at  one  end,  as  2  and  2  make  5,  and  necessity 
at  the  other,  as  2  and  2  make  4,  and  a  graduated  rise  of  examples 
between  them.  Down  came  a  blow  :  '  What !  put  necessary  and 
contingent  propositions  together  !  It's  absurd  !'  I  pointed  out  that 
the  two  kinds  of  necessity  are  but  such  extremes  of  probability  as 

0  and  co  are  of  number,  and  illustrated  by  an  urn  with  1  white 
and  n  black  balls,  n  increasing  without  limit.     It  was  frankly 
seen,  and  the  point  yielded ;  a  large  company  was  present- 
Again,  in  a  large   party,  after  dinner,  and   politics  being  the 

subject,  I  was  proceeding,  in  discussion  with  Mr.  Whewell,  with 
1 1  think'  .  .  . — '  Ugh  !  you  think  !'  was  the  answer.  I  repeated 
my  phrase,  and  gave  as  a  reason  the  words  which  Lord  Grey  had 
used  in  the  House  of  Lords  the  night  before  (the  celebrated 
advice  to  the  Bishops  to  set  their  houses  in  order).  He  had  not 
heard  of  this,  and  his  manner  changed  in  an  instant :  he  was 
the  rational  discutient  all  the  rest  of  the  evening,  having  pre- 
viously been  nothing  but  a  disputant  with  all  the  distinctions 
strongly  marked. 

I  have  said  that  Whewell  was  gentle  with  his  pupils ;  it  was 
the  same  with  all  who  wanted  teaching :  it  was  only  on  an  armed 
enemy  that  he  drew  his  weapon.  The  letter  which  he  wrote  to 
Mr.  J.  Smith  is  an  instance :  and  as  it  applies  with  perfect 
fidelity  to  the  efforts  of  unreasoning  above  described,  I  give  it 
here.  Mr.  James  Smith  is  skilfully  exposed,  and  felt  it ;  as  is 
proved  by  '  putting  the  writer  in  the  stocks.' — 

The  Lodge,  Cambridge,  September  14th,  1862. 

Sir, — I  have  received  your  explanation  of  your  proposition  that  the 
circumference  of  the  circle  is  to  its  diameter  as  25  to  8.  I  am  afraid 

1  shall  disappoint  you  by  saying  that  I  see  no  force  in  your  proof :  and 
I  should  Lope  that  you  will  see  that  there  is  no  force  in  it  if  you  con- 
sider this  : — In  the  whole  course  of  the  proof,  though  the  word  circle 
occurs,  there  is  no  property  of  the  circle  employed.     You  may  do  this  : 
you   may  put  the  word    hexagon   or   dodecagon,   or   any  other   word 
describing  a  polygon  in  tbe  place  of  Circle  in  your  proof,  and  the  proof 
would  be  just  as  good  as  before.     Does  not  this  satisfy  you  that  you 

annot  have  proved  a  property  of  that  special  figure — a  circle  ? 


AN   M.P/S   ARITHMETIC.  417 

Or  you  may  do  this  :  calculate  the  side  of  a  polygon  of  24  sides 
inscribed  ia  a  circle.  I  think  you  are  a  Mathematician  enough  to  do 
this.  You  will  find  that  if  the  radius  of  the  circle  be  one,  the  side  of 
this  polygon  is  "264  &c.  Now,  the  arc  which  this  side  subtends  is 
according  to  your  proposition  ~~  =  '2604,  and  therefore  the  chord  is 
greater  than  its  arc,  which  you  will  allow  is  impossible. 
I  shall  be  glad  if  these  arguments  satisfy  you,  and 

I  am,  Sir,  your  obedient  Servant, 

W.  WHEWELL. 


In  the  debate  of  May,  1866,  on  Electoral  Qualifications,  a 
question  arose  about  arithmetical  capability.  Mr.  Gladstone 
asked  how  many  members  of  the  House  could  divide  1330L  17s.  6d. 
by  21.  13s.  8d.  Six  hundred  and  fifty-eight,  answered  one  mem- 
ber ;  the  thing  cannot  be  done,  answered  another.  There  is  an 
old  paradox  to  which  this  relates  :  it  arises  out  of  the  ignorance 
of  the  distinction  between  abstract  and  concrete  arithmetic. 
Magnitude  may  be  divided  by  magnitude ;  and  the  answer  is 
number:  how  often  does  1 2d.  contain  4c£. ;  answer  three  times. 
Magnitude  may  be  divided  by  number,  and  the  answer  is  magni- 
tude :  I2d.  is  divided  in  four  equal  parts,  what  is  each  part  ? 
Answer  three  pence.  The  honourable  objector,  whose  name  I 
suppress,  trusting  that  he  has  mended  his  ways,  gave  the  follow- 
ing utterance : — 

"  With  regard  to  the  division  sum,  it  was  quite  possible  to  divide  by 
a  sum,  but  not  by  money.  How  could  any  one  divide  money  by 
21.  16s.  8d.  ?  (Laughter.)  The  question  might  be  asked,  '  How  many 
times  2s.  will  go  into  1Z.  ?'  but  that  was  not  dividing  by  money;  it 
was  simply  dividing  20  by  2.  He  might  be  asked,  '  How  many  times 
will  6s.  8d.  go  into  a  pound  ? '  but  it  was  only  required  to  divide  240 
by  80.  If  the  right  hon.  gentleman  were  to  ask  the  hon.  member  for 
Brighton  (Professor  Fawcett),  or  any  other  authority,  he  would  receive 
the  same  answer — viz..  that  it  was  possible  to  divide  by  a  sum,  but 
not  by  money.  (Hear.)  " 

I  shall  leave  all  comment  for  my  second  edition,  if  I  publish 
one.  I  shall  be  sure  to  have  something  to  laugh  at.  Anything 
said  from  a  respectable  quarter,  or  supposed  to  be  said,  is  sure  to 
find  defenders.  Sam  Johnson,  a  sound  arithmetician,  comparing 
himself,  and  what  he  alone  had  done  in  three  years,  with  the  forty 
French  Academicians  and  their  forty  years,  said  it  proved  that  an 
Englishman  is  to  a  Frenchman  as  40  x  40  to  3,  or  as  1600  to  3. 
Boswell,  who  was  no  great  hand  at  arithmetic,  made  him  say  that 


E  E 


418  A   BUDGET   OF  PARADOXES. 

an  Englishman  is  to  a  Frenchman  as  3  to  1 600.  When  I  pointed 
this  out,  the  supposed  Johnson  was  defended  through  thick  and 
thin  in  Notes  and  Queries. 

I  am  now  curious  to  see  whether  the  following  will  find  a 
palliator.  It  is  from  'Tristram  Shandy,'  book  v.  chapter  3. 
There  are  two  curious  idioms,  '  for  for '  and  '  half  in  half ; '  but 
these  have  nothing  to  do  with  my  point : — 

'  A  blessing  which  tied  up  my  father's  tongue,  and  a  misfortune 
which  set  it  loose  with  a  good  grace,  were  pretty  equal :  sometimes, 
indeed,  the  misfortune  was  the  better  of  the  two  ;  for,  for  instance, 
where  the  pleasure  of  the  harangue  was  as  ten,  and  the  pain  of  the 
misfortune  but  &sfve,  my  father  gained  half  in  half;  and  consequently 
was  as  well  again  off  as  if  it  had  never  befallen  him.' 

This  is  a  jolly  confusion  of  ideas ;  and  wants  nothing  but  a 
defender  to  make  it  perfect.  A  person  who  invests  five  with  a 
return  of  ten,  and  one  who  loses  five  with  one  hand  and  gains  ten 
with  the  other,  both  leave  off  five  richer  than  they  began,  no 
doubt.  The  first  gains  '  half  in  half,'  more  properly  l  half  on 
half,'  that  is,  of  the  return,  10,  the  second  5  is  gain  upon  the 
first5  invested.  'Half  in  half '  is  a  queer  way  of  saying  cent, 
per  cent.  If  the  51.  invested  be  all  the  man  had  in  the  world, 
he  comes  out,  after  the  gain,  twice  as  well  off  as  he  began,  with 
reference  to  his  whole  fortune.  But  it  is  very  odd  to  say  that 
balance  of  51.  gain  is  twice  as  good  as  if  nothing  had  befallen, 
either  loss  or  gain.  A  mathematician  thinks  5  an  infinite 
number  of  times  as  great  as  0.  The  whole  confusion  is  not  so 
apparent  when  money  is  in  question :  for  money  is  money  whether 
gained  or  lost.  But  though  pleasure  and  pain  stand  to  one 
another  in  the  same  algebraical  relation  as  money  gained  and 
lost,  yet  there  is  more  than  algebra  can  take  account  of  in  the 
difference. 

Next,  Ei.  Milward  (Kichard,  no  doubt,  but  it  cannot  be  proved) 
who  published  Selden's  Table  Talk,  which  he  had  collected  while 
serving  as  amanuensis,  makes  Selden  say,  '  A  subsidy  was  counted 
the  fifth  part  of  a  man's  estate  ;  and  so  fifty  subsidies  is  five  and 
and  forty  times  more  than  a  man  is  worth.'  For  times  read  sub- 
sidies, which  seems  part  of  the  confusion,  and  there  remains  the 
making  all  the  subsidies  equal  to  the  first,  though  the  whole  of 
which  they  are  to  be  the  fifths  is  perpetually  diminished. 

Thirdly,  there  is  the  confusion  of  the  great  misomath  of  our 
o.wn  day,  who  discovered  two  quantities  which  he  avers  to  be 


ERRONEOUS   ARITHMETICAL   NOTIONS.  419 

identically  the  same,  but  the  greater  the  one  the  less  the  other. 
He  had  a  truth  in  his  mind,  which  his  notions  of  quantity  were 
inadequate  to  clothe  in  language.  This  erroneous  phraseology  has 
not  found  a  defender ;  and  I  am  almost  inclined  to  say,  with 
Falstaff,  The  poor  abuses  of  the  time  want  countenance. 

'  Shallow  numerists,'  as  Cocker  is  made  to  call  them,  have  long 
been  at  work  upon  the  question  how  to  multiply  money  by  money. 
It  is,  I  have  observed,  a  very  common  way  of  amusing  the  taedium 
of  a  sea  voyage  :  I  have  had  more  than  one  bet  referred  to  me. 
Because  an  oblong  of  five  inches  by  four  inches  contain  5x4 
or  20  square  inches,  people  say  that  five  inches  multiplied  by  four 
inches  is  twenty  square  inches  :  and,  thinking  that  they  have 
multiplied  length  by  length,  they  stare  when  they  are  told  that 
money  cannot  be  multiplied  by  money.  One  of  my  betters  made  it 
an  argument  for  the  thing  being  impossible,  that  there  is  no  square 
money :  what  could  I  do  but  suggest  that  postage-stamps  should 
be  made  legal  tender.  Multiplication  must  be  repetition :  the 
repeating  process  must  be  indicated  by  number  of  times.  I  once 
had  difficulty  in  persuading  another  of  my  betters  that  if  you  repeat 
five  shillings  as  often  as  there  are  hairs  in  a  horse's  tail,  you  do 
not  multiply  Jive  shillings  by  a  horsetail. 

I  am  very  sorry  to  say  that  these  wrong  notions  have  found 
support — I  think  they  do  so  no  longer — in  the  University  of 
Cambridge.  In  1856  or  1857,  an  examiner  was  displaced  by  a 
vote  of  the  Senate.  The  pretext  was  that  he  was  too  severe  an 
examiner  :  but  it  was  well  known  that  great  dissatisfaction  had 
been  expressed,  far  and  wide  through  the  Colleges,  at  an  absurd 
question  which  he  had  given.  He  actually  proposed  such  a 
fraction  as 

68.  3d. 
1 7s.  4d. 

As  common  sense  gained  a  hearing  very  soon,  there  is  no 
occasion  to  say  more.  In  1858,  it  was  proposed  at  a  college  ex- 
amination, to  divide  22557  days,  20  hours,  20  minutes,  48 
seconds,  by  57  minutes,  12  seconds,  and  also  to  explain  the 
fraction 

32£.  188.  Sd. 

G'2l.  12s.  9<Z. 

All  paradoxy,  in  matters  of  demonstration,  arises  out  of  muddle 
about  first  principles.  Who  can  say  how  much  of  it  is  to  be  laid 
at  the  door  of  the  University  of  Cambridge,  for  not  taking  care 
of  the  elements  of  arithmetical  thought  ? 


420  A  BUDGET  OF  PARADOXES. 

The  phenomena  of  the  two  ends  of  society,  when  brought  to- 
gether, give  interesting  comparisons :  I  mean  the  early  beginnings 
of  thought  and  literature,  and  our  own  high  and  finished  state,  as 
we  think  it.  There  is  one  very  remarkable  point.  In  the  early 
day,  the  letter  was  matter  of  the  closest  adherence,  and  implied 
meanings  were  not  admitted. 

The  blessing  of  Isaac  meant  for  Esau,  went  to  false  Jacob,  in 
spite  of  the  imposition  ;  and  the  writer  of  Grenesis  seems  to  intend 
to  give  the  notion  that  Isaac  had  no  power  to  pronounce  it  null 
and  void.  And  '  Jacob's  policy,  whereby  he  became  rich ' — as 
the  chapter-heading  puts  it— in  speckled  and  spotted  stock,  is 
not  considered  as  a  violation  of  the  agreement,  which  contemplated 
natural  proportions.  In  the  story  of  Lycurgus  the  lawgiver  is 
held  to  have  behaved  fairly  when  he  bound  the  Spartans  to  obey 
his  laws  until  he  returned — intimating  a  short  absence — he 
intending  never  to  return.  And  Vishnoo,  when  he  asked  the 
usurper  for  three  steps  of  territory  as  a  dwarf,  and  then  enlarged 
himself  until  he  could  bring  heaven  and  earth  under  the  bargain, 
was  thought  clever,  certainly,  but  quite  fair. 

There  is  nothing  of  this  kind  recognised  in  our  day :  so  far 
good.  But  there  is  a  bad  contrary :  the  age  is  apt,  in  interpre- 
tation, to  upset  the  letter  in  favour  of  the  view — very  often  the 
after  thought — of  one  side  only.  The  case  of  John  Palmer,  the 
improver  of  the  mail  coach  system,  is  smothered.  He  was  to 
have  an  office  and  a  salary,  and  2£  per  cent,  for  life  on  the  in- 
creased revenue  of  the  Post-Office.  His  rights  turned  out  so 
large,  that  Government  would  not  pay  them.  For  misconduct, 
real  or  pretended,  they  turned  him  out  of  his  office, :  but  his 
bargain  as  to  the  percentage  had  nothing  to  do  with  his  future 
conduct ;  it  was  payment  for  his  plan.  I  know  nothing,  except 
from  the  debates  of  1808  in  the  two  Houses:  if  any  one  can 
redeem  the  credit  of  the  nation,  the  field  is  open.  When  I  was 
young,  the  old  stagers  spoke  of  this  transaction  sparingly,  and 
dismissed  it  speedily. 

The  government  did  not  choose  to  remember  what  private 
persons  must  remember,  and  are  made  to  remember,  if  needful. 
When  Dr.  Lardner  made  his  bargain  with  the  publishers  for  the 
Cabinet  Cyclopcedia  he  proposed  that  he,  as  editor,  should  have 
a  certain  sum  for  every  hundred  sold  above  a  certain  number : 
the  publishers,  who  did  not  think  there  was  any  chance  of  reach- 
ing the  turning  sale  of  this  stipulation,  readily  consented.  But 
it  turned  out  that  Dr.  Lardner  saw  further  than  they :  the  re- 
turns under  this  stipulation  gave  him  a  very  handsome  addition 


DECLARATION   OF   BELIEF.  421 

to  his  other  receipts.  The  publishers  stared ;  but  they  paid. 
They  had  no  idea  of  standing  out  that  the  amount  was  too  much 
for  an  editor  ;  they  knew  that,  though  the  editor  had  a  per- 
centage, they  had  all  the  rest ;  and  they  would  not  have  felt 
aggrieved  if  he  had  received  ten  times  as  much.  But  govern- 
ments, which  cannot  be  brought  to  book  before  a  sworn  jury,  are 
ruled  only  by  public  opinion.  John  Palmer's  day  was  also  the 
day  of  Thomas  Fyshe  Palmer,  and  the  governments,  in  their 
prosecutions  for  sedition,  knew  that  these  would  have  a  reflex 
action  upon  the  minds  of  all  who  wrote  about  public  affairs. 


1864—65. — It  often  happens  that  persons  combine  to  maintain 
and  enforce  an  opinion  ;  but  it  is,  in  our  state  of  society,  a  para- 
dox to  unite  for  the  sole  purpose  of  blaming  the  opposite  side. 
To  invite  educated  men  to  do  this,  and  above  all,  men  of  learning 
or  science,  is  the  next  paradoxical  thing  of  all.  But  this  was 
done  by  a  small  combination  in  1864.  They  got  together  and 
drew  up  a  declaration,  to  be  signed  by  '  students  of  the  natural 
sciences,'  who  were  to  express  their  '  sincere  regret  that  researches 
into  scientific  truth  are  perverted  by  some  in  our  own  times  into 
occasion  for  casting  doubt  upon  the  truth  and  authenticity  of  the 
Holy  Scriptures.'  In  words  of  ambiguous  sophistry,  they  pro- 
ceeded to  request,  in  effect,  that  people  would  be  pleased  to  adopt 
the  views  of  churches  as  to  the  complete  inspiration  of  all  the 
canonical  books.  The  great  question  whether  the  Word  of  Grod 
is  in  the  Bible,  or  whether  the  Word  of  Grod  is  all  the  Bible, 
was  quietly  taken  for  granted  in  favour  of  the  second  view ;  to  the 
end  that  men  of  science  might  be  induced  to  blame  those  who 
took  the  first  view.  The  first  public  attention  was  drawn  to  the 
subject  by  Sir  John  Herschel,  who  in  refusing  to  sign  the  writ 
sent  to  him,  administered  a  rebuke  in  the  Athenceum,  which 
would  have  opened  most  eyes  to  see  that  the  case  was  hopeless. 
The  words  of  a  man  whose  suaviter  in  tnodo  makes  his  fortiter 
in  re  cut  blocks  with  a  razor  are  worth  preserving: — 

'  I  consider  the  act  of  calling  upon  me  publicly  to  avow  or  disavow, 
to  approve  or  disapprove,  in  writing,  any  religious  doctrine  or  state- 
ment, however  carefully  or  cautiously  drawn  up  (in  other  words,  to 
append  my  name  to  a  religious  manifesto)  to  be  an  infringement  of 
that  social  forbearance  which  guards  the  freedom  of  religious  opinion 
in  this  country  with  especial  sanctity  ...  I  consider  this  movement 
simply  mischievous,  having  a  direct  tendency  (by  putting  forward  a 
new  Shibboleth,  a  new  verbal  test  of  religious  partisanship)  to  add  a 


422  A   BUDGET   OF  PAKADOXES. 

fresh  element  of  discord  to  the  already  too  discordant  relations  of  the 
Christian  world  .  .  .  But  -no  nicety  of  wording,  no  artifice  of  human 
language,  will  suffice  to  discriminate  the  hundredth  part  of  the  shades 
of  meaning  in  which  the  most  world-wide  differences  of  thought  on 
such  subjects  may  be  involved  ;  or  prevent  the  most  gently  worded 
and  apparently  justifiable  expression  of  regret,  so  embodied,  from 
grating  on  the  feelings  of  thousands  of  estimable  and  well-intentioned 
men  with  all  the  harshness  of  controversial  hostility.' 


Other  doses  were  administered  by  Sir  J.  Bowring,  Sir  W.  Rowan 
Hamilton,  and  myself.  The  signed  declaration  was  promised  for 
Christmas,  1864:  but  nothing  presentable  was  then  ready;  and 
it  was  near  Midsummer,  1865,  before  it  was  published.  Persons 
often  incautiously  put  their  names  without  seeing  the  character 
of  a  document,  because  they  coincide  in  its  opinions.  In  this 
way,  probably,  fifteen  respectable  names  were  procured  before 
printing ;  and  these,  when  committed,  were  hawked  as  part  of  an 
application  to  '  solicit  the  favour '  of  other  signatures.  It  is 
likely  enough  no  one  of  the  fifteen  saw  that  the  declaration  was, 
not  maintenance  of  their  own  opinion,  but  regret  (a  civil  word 
for  blame}  that  others  should  think  differently. 

When  the  list  appeared,  there  were  no  fewer  than  716  names! 
But  analysis  showed  that  this  roll  was  not  a  specimen  of  the 
mature  science  of  the  country.  The  collection  was  very  miscel- 
laneous :  38  were  designated  as  '  students  of  the  College  of 
Chemistry,'  meaning  young  men  who  attended  lectures  in  that 
college.  But  as  all  the  Royal  Society  had  been  applied  to,  a  test 
results  as  follows.  Of  Fellows  of  the  Royal  Society,  600  in 
number,  62  gave  their  signatures  ;  of  writers  in  the  Philosophical 
Transactions,  166  in  number,  19  gave  their  signatures.  Roughly 
speaking,  then,  only  one  out  of  ten  could  be  got  to  express 
disapprobation  of  the  free  comparison  of  the  results  of  science 
with  the  statements  of  the  canonical  books.  And  I  am  satisfied 
that  many  of  these  thought  they  were  signing  only  a  declaration 
of  difference  of  opinion,  not  of  blame  for  that  difference.  The 
number  of  persons  is  not  small  who,  when  it  comes  to  signing 
printed  documents,  would  put  their  names  to  a  declaration  that 
the  coffee-pot  ought  to  be  taken  downstairs,  meaning  that  the 
teapot  ought  to  be  brought  up-stairs.  And  many  of  them  would 
defend  it.  Some  would  say  that  the  two  things  are  not  contra- 
dictory ;  which,  with  a  snort  or  two  of  contempt,  would  be  very 
effective.  Others  would,  in  the  candid  and  quiet  tone,  point  out 
that  it  is  all  one,  because  coffee  is  usually  taken  before  tea,  and  it 


DECLARATION   OF   BELIEF. 


423 


keeps  the  table  clear  to  send  away  the  coffee-pot  before  the  teapot 
is  brought  up. 

The  original  signatures  were  decently  interred  in  the  Bodleian 
Library :  and  the  advocates  of  scattering  indefinite  blame  for 
indefinite  sins  of  opinion  among  indefinite  persons  are,  I  under- 
stand, divided  in  opinion  about  the  time  at  which  the  next 
attempt  shall  be  made  upon  men  of  scientific  studies  :  some  are 
for  the  Greek  Calends,  and  others  for  the  Roman  Olympiads. 
But,  with  their  usual  love  of  indefiniteness,  they  have  deter- 
mined that  the  choice  shall  be  argued  upon  the  basis  that  which 
comes  first  cannot  be  settled,  and  is  of  no  consequence. 

I  give  the  declaration  entire,  as  a  curiosity  :  and  parallel  with  it 
I  give  a  substitute  which  was  proposed  in  the  Athenaeum,  as 
worthy  to  be  signed  both  by  students  of  theology,  and  by  students 
of  science,  especially  in  past  time.  When  a  new  attempt  is  made, 
it  will  be  worth  while  to  look  at  both  : — 


Declaration. 

WE,  the  undersigned  Students 
of  the  Natural  Sciences,  desire  to 
express  our  sincere  regret,  that 
researches  into  scientific  truth  are 
perverted  by  some  in  our  own 
times  into  occasion  for  casting 
doubt  upon  the  Truth  and  Au- 
thenticity of  the  Holy  Scriptures. 

We  conceive  that  it  is  impossible 
for  the  Word  of  God,  as  written 
in  the  book  of  nature,  and  God's 
Word  written  in  Holy  Scripture, 
to  contradict  one  another,  how- 
ever much  they  may  appear  to 
differ. 

We  are  not  forgetful  that  Physical 
Science  is  not  complete,  but  is 
only  in  a  condition  of  progress, 
and  that  at  present  our  finite 
reason  enables  us  only  to  see  as 
through  a  glass  darkly, 


Proposed  Substitute. 

WE,  the  undersigned  Students 
of  Theology  and  of  Nature,  desire 
to  express  our  sincere  regret,  that 
common  notions  of  religious  truth 
are  perverted  by  some  in  our  own 
times  into  occasion  for  casting 
reproach  upon  the  advocates  of 
demonstrated  or  highly  probable 
scientific  theories. 
We  conceive  that  it  is  impossible 
for  the  Word  of  God,  as  correctly 
read  in  the  Book  of  Nature,  and 
the  Word  of  God,  as  truly  inter- 
preted out  of  the  Holy  Scripture, 
to  contradict  one  another,  how- 
ever much  they  may  appear  to 
differ. 

We  are  not  forgetful  that  neither 
theological  interpretation  nor 
physical  knowledge  is  yet  com- 
plete, but  that  both  are  in  a  con- 
dition of  progress ;  and  that  at 
present  our  finite  reason  enables 
us  only  to  see  both  one  and  the 
other  as  through  a  glass  darkly 
[the  writers  of  the  original  de- 


424 


A  .BUDGET   OF  PARADOXES. 


and  we  confidently  believe,  that 
a  time  will  come  when  the  two 
records  will  be  seen  to  agree  in 
every  particular. 

We  cannot  but  deplore  that  Na- 
tural Science  should  be  looked 
upon  with  suspicion  by  many 
who  do  not  make  a  study  of  it, 
merely  on  account  of  the  unad- 
vised manner  in  which  some  are 
placing  it  in  opposition  to  Holy 
Writ. 


We  believe  that  it  is  the  duty  of 
every  Scientific  Student  to  inves- 
tigate nature  simply  for  the  pur- 
pose of  elucidating  truth, 


and  that  if  he  finds  that  some  of 
his  results  appear  to  be  in  con- 
tradiction to  the  Written  Word, 
or  rather  to  his  own  interpreta- 
tions of  it,  which  may  be  erroneous, 
he  should  not  presumptuously 
affirm  that  his  own  conclusions 
must  be  right,  and  the  statements 
of  Scripture  wrong  : 

rather,  leave  the  two  side  by  side 

till  it  shall  please  God  to  allow  us 
to  see  the  manner  in  which  they 
may  be  reconciled ; 
and,    instead    of    insisting    upon 


claration  have  distinctively  ap- 
plied to  physical  science  the 
phrase  by  which  St.  Paul  denotes 
the  imperfections  of  theological 
vision,  which  they  tacitly  assume 
to  be  quite  perfect], 
and  we  confidently  believe  that 
a  time  will  come  when  the  two 
records  will  be  seen  to  agree  in 
every  particular. 

We  cannot  but  deplore  that  Re- 
ligion should  be  looked  upon 
with  suspicion  by  some,  and 
Science  by  others,  of  the  student  s 
of  either  who  do  not  make  a  study 
of  the  other,  merely  on  account 
of  the  unadvised  manner  in  which 
some  are  placing  Religion  in  op- 
position to  Science,  and  some  are 
placing  Science  in  opposition  to 
Religion. 

We  believe  that  it  is  the  duty  of 
every  theological  student  to  in- 
vestigate the  Scripture,  and  of 
every  scientific  student  to  inves- 
tigate Nature,  simply  for  the 
purpose  of  elucidating  truth. 
And  if  either  should  find  that 
some  of  his  results  appear  to 
be  in  contradiction,  whether  to 
Scripture  or  to  Nature,  or  rather 
to  his  own  interpretation  of  one 
or  the  other,  which  may  be 
erroneous,  he  should  not  affirm 
as  with  certainty  that  his  own 
conclusion  must  be  right,  and 
the  other  interpretation  wrong : 
but  should  leave  the  two  side  by 
side  for  further  inquiry  into  both, 
until  it  shall  please  God  to  allow 
us  to  arrive  at  the  manner  in 
which  they  may  be  reconciled. 
In  the  mean  while,  instead  of 
insisting,  and  least  of  all  with 
acrimony  or  injurious  statements 
about  others,  upon  the  seeming 


DECLARATION   OF  BELIEF.  425 

the  seeming  differences  between  differences  between  Science  and 
Science  and  the  Scriptures,  it  the  Scriptures,  it  would  be  a 
would  be  as  well  to  rest  in  faith  thousand  times  better  to  rest  in 
upon  the  points  in  which  they  faith  as  to  our  future  state,  in 
agree.  hope  as  to  our  coming  know- 

ledge,  and  in  charity  as  to  our 
present  differences. 

The  distinctness  of  the  fallacies  is  creditable  to  the  composers, 
and  shows  that  scientific  habits  tend  to  clearness,  even  to  sophistry. 
Nowhere  does  it  so  plainly  stand  out  that  the  Written  Word 
means  the  sense  in  which  the  accuser  takes  it,  while  the  sense  of 
the  other  side  is  their  interpretation.  The  infallible  church  on 
one  side,  arrayed  against  heretical  pravity  on  the  other,  is  seen  in 
all  subjects  in  which  men  differ.  At  school  there  were  various 
games  in  which  one  or  another  advantage  was  the  right  of  those 
who  first  called  for  it.  In  adult  argument  the  same  thing  is  often 
attempted  :  we  often  hear — I  cried  Church  first ! 

I  end  with  the  answer  which  I  myself  gave  to  the  application  : 
its  revival  may  possibly  save  me  from  a  repetition  of  the  like.  If 
there  be  anything  I  hate  more  than  another  it  is  the  proposal 
to  place  any  persons,  especially  those  who  allow  freedom  to  me, 
under  any  abridgment  of  their  liberty  to  think,  to  infer,  and  to 
publish.  If  they  break  the  law,  take  the  law  ;  but  do  not  make 
the  law :  cuyopaiot  djovrai  eyKaXsirwcrav  a\\rj\oi$.  I  would  rather 
be  asked  to  take  shares  in  an  argyrosteretic  company  (with 
limited  liability)  for  breaking  into  houses  by  night  on  fork  and 
spoon  errands.  I  should  put  aside  this  proposal  with  nothing  but 
laughter.  It  was  a  joke  against  Sam  Rogers  that  his  appearance 
was  very  like  that  of  a  corpse.  The  John  Bull  newspaper — 
suppose  we  now  say  Theodore  Hook — averred  that  when  he 
hailed  a  coach  one  night  in  St.  Paul's  Churchyard,  the  jarvey 
said,  '  Ho  !  ho  !  my  man  ;  I'm  not  going  to  be  taken  in  that  way : 
go  back  to  your  grave ! '  This  is  the  answer  I  shall  make  for  the 
future  to  any  relics  of  a  former  time  who  shall  want  to  call  me  off 
the  stand  for  their  own  purposes.  What  obligation  have  I  to 
admit  that  they  belong  to  our  world  ? 


4'26  A  BUDGET  OF  PARADOXES. 

"SCEIPTUKE   AND   SCIENCE. 

"  The  Writ  De  Hceretico  Commiserando. 

Nov.  14,  1864. 

"  THIS  document  was  sent  to  me  four  days  ago.  It  '  solicits  the 
favour ' — I  thought  at  first  it  was  a  grocer's  supplication  for  tea 
and  sugar  patronage — of  my  signature  to  expression  of  *  sincere 
regret '  that  some  persons  unnamed — general  warrants  are  illegal 
— differ  from  what  I  am  supposed — by  persons  whom  it  does  not 
concern — to  hold  abcut  Scripture  and  Science  in  their  real  or 
alleged  discrepancies. 

"  No  such  favour  from  me  :  for  three  reasons.  First,  I  agree 
with  Sir  J.  Herschel  that  the  solicitation  is  an  intrusion  to  be 
publicly  repelled.  Secondly,  I  do  not  regret  that  others  should 
differ  from  me,  think  what  I  may  :  those  others  are  as  good  as  I, 
and  as  well  able  to  think,  and  as  much  entitled  to  their  con- 
clusions. Thirdly,  even  if  I  did  regret,  I  should  be  ashamed  to 
put  my  name  to  bad  chemistry  made  to  do  duty  for  good  reason- 
ing. The  declaration  is  an  awkward  attempt  to  saturate  sophism 
with  truism  ;  but  the  sophism  is  left  largely  in  excess. 

"  I  owe  the  inquisitors  a  grudge  for  taking  down  my  conceit  of 
myself.  For  two  months  I  have  crowed  in  niy  own  mind  over  my 
friend  Sir  J.  Herschel,  fancying  that  the  promoters  instinctively 
knew  better  than  to  bring  their  fallacies  before  a  writer  on  logic. 
Ah  !  my  dear  Sir  John !  thought  I,  if  you  had  shown  yourself  to 
be  well  up  in  Barbara  Celarent,  and  had  ever  and  anon  astonished 
the  natives  with  the  distinction  between  simpliciter  and  secun- 
dum  quid,  no  autograph-hunters  would  have  baited  a  trap  with 
non  sequitur  to  catch  your  signature.  What  can  I  say  now  ?  I 
hide  my  diminished  head,  diminished  by  the  horns  which  I  have 
been  compelled  to  draw  in. 

"  Those  who  make  personal  solicitation  for  support  to  an  opinion 
about  religion  are  bound  to  know  their  men.  The  king  had  a 
right  to  Brother  Neale's  money,  because  Brother  Neale  offered  it. 
Had  he  put  his  hand  into  purse  after  purse  by  way  of  finding  out 
all  who  were  of  Brother  Neale's  mind,  he  would  have  been  justly 
met  by  a  rap  on  the  knuckles  whenever  he  missed  his  mark. 

u  The  kind  of  test  before  me  is  the  utmost  our  time  will  allow  of 
that  inquisition  into  opinion  which  has  been  the  curse  of  Chris- 
tianity ever  since  the  State  took  Providence  under  its  protection. 


DECLAKATION   OF   BELIEF.  427 

The  writ  de  hceretico  commiserando  is  little  more  than  the  smell 
of  the  empty  cask :  and  those  who  issue  it  may  represent  the  old 
woman  with  her 

O  suavis  anima,  quale  in  te  dicara  bonum 
Antehac  fuisse  ;  tales  cnm  sint  reliquiae. 

It  is  no  excuse  that  the  illegitimate  bantling  is  a  very  little  one. 
Its  parents  may  think  themselves  hardly  treated  when  they  are 
called  lineal  successors  of  Tony  Fire-the-faggot :  but,  degenerate 
though  they  be,  such  is  their  ancestry.  Let  every  allowance  be 
made  for  them :  but  their  unholy  fire  must  be  trodden  out ;  so 
long  as  a  spark  is  left,  nothing  but  fuel  is  wanted  to  make  a 
blaze.  If  this  cannot  be  done,  let  the  flame  be  confined  to 
theology,  though  even  there  it  burns  with  diminished  vigour  :  and 
let  charity,  candour,  sense,  and  ridicule,  be  ready  to  play  upon  it 
whenever  there  is  any  chance  of  its  extending  to  literature  or 
science. 

"  What  would  be  the  consequence  if  this  test-signing  absurdity 
were  to  grow  ?  Deep  would  call  unto  deep  ;  counter-declaration 
would  answer  declaration,  each  stronger  than  the  one  before. 
The  moves  would  go  on  like  the  dispute  of  two  German  students, 
of  whom  each  is  bound  to  a  sharper  retort  on  a  graduated  scale, 
until  at  last  comes  dummer  junge  ! — and  then  they  must  fight. 
There  is  a  gentleman  in  the  upper  fifteen  of  the  signers  of  the 
writ — the  hawking  of  whose  names  appears  to  me  very  bad  taste 
— whom  I  met  in  cordial  co-operation  for  many  a  year  at  a 
scientific  board.  All  I  knew  about  his  religion  was  that  he,  as  a 
clergyman,  must  in  some  sense  or  other  receive  the  39  Articles  : 
— all  that  he  could  know  about  mine  was  that  I  was  some  kind  of 
heretic,  or  so  reputed.  If  we  had  come  to  signing  opposite 
manifestoes,  turn-about,  we  might  have  found  ourselves  in  the 
lowest  depths  of  party  discussion  at  our  very  council-table.  I 
trust  the  list  of  subscribers  to  the  declaration,  when  it  comes  to 
be  published,  will  show  that  the  bulk  of  those  who  have  really 
added  to  our  knowledge  have  seen  the  thing  in  its  true  light. 

"  The  promoters — I  say  nothing  about  the  subscribers — of  the 
movement  will,  I  trust,  not  feel  aggrieved  at  the  course  I  have 
taken  or  the  remarks  I  have  made.  Walter  Scott  says  that  before 
we  judge  Napoleon  by  the  temptation  to  which  he  yielded,  we 
ought  to  remember  how  much  he  may  have  resisted  :  I  invite 
them  to  apply  this  rule  to  myself;  they  can  have  no  idea  of  the 
feeling  with  which  I  contemplate  all  attempts  to  repress  freedom 


428  A  BUDGET  OF  PARADOXES. 

of  inquiry,  nor  of  the  loathing  with  which  I  recoil  from  the 
proposal  to  be  art  and  part.  They  have  asked  me  to  give  a 
public  opinion  upon  a  certain  point.  It  is  true  that  they  have 
had  the  kindness  to  tender  both  the  opinion  they  wish  me  to 
form,  and  the  shape  in  which  they  would  have  it  appear  :  I  will 
let  them  draw  me  out,  but  I  will  not  let  them  take  me  in.  If 
they  will  put  an  asterisk  to  my  name,  and  this  letter  to  the 
asterisk,  they  are  welcome  to  my  signature.  As  I  do  not  expect 
them  to  relish  this  proposal,  I  will  not  solicit  the  favour  of  its 
adoption.  But  they  have  given  a  right  to  think,  for  they  have 
asked  me  to  think  ;  to  publish,  for  they  have  asked  me  to  allow 
them  to  publish  ;  to  blame  them,  for  they  have  asked  me  to 
blame  their  betters.  Should  they  venture  to  find  fault  because 
my  direction  of  disapproval,  publicly  given,  is  half  a  revolution 
different  from  theirs,  they  will  be  known  as  having  presented  a 
loaded  document  at  the  head  of  a  traveller  in  the  highway  of 
discussion,  with — Your  signature  or  your  silence  I  " 


The  paradox  being  the  proposition  of  something  which  runs 
counter  to  what  would  generally  be  thought  likely,  may  present 
itself  in  many  ways.  There  is  a  fly-leaf  paradox,  which  puzzled 
me  for  many  years,  until  I  found  a  probable  solution.  I  fre- 
quently saw,  in  the  blank  leaves  of  old  books,  learned  books, 
Bibles  of  a  time  when  a  Bible  was  very  costly,  &c.,  the  name  of 
an  owner  who,  by  the  handwriting  and  spelling,  must  have  been 
an  illiterate  person  or  a  child,  followed  by  the  date  of  the  book 
itself.  Accordingly,  this  uneducated  person  or  young  child 
seemed  to  be  the  first  owner,  which  in  many  cases  was  not  credible. 
Looking  one  day  at  a  Barker's  Bible  of  1599,  I  saw  an  inscription 
in  a  child's  writing,  which  certainly  belonged  to  a  much  later 
date.  It  was  '  Martha  Taylor,  her  book,  giuen  me  by  Granny 
Scott  to  keep  for  her  sake.'  With  this  the  usual  verses,  followed 
by  1599,  the  date  of  the  book.  But  it  so  chanced  that  the  blank 
page  opposite  the  title,  on  which  the  above  was  written,  was  a 
verso  of  the  last  leaf  of  a  prayer  book,  which  had  been  bound 
before  the  Bible  ;  and  on  the  recto  of  this  leaf  was  a  colophon, 
with  the  date  1632.  It  struck  me  immediately  that  uneducated 
persons  and  children,  having  seen  dates  written  under  names,  and 
not  being  quite  up  in  chronology,  did  frequently  finish  off  with 
the  date  of  the  book,  which  stared  them  in  the  face. 

Always  write  in  your  books.  You  may  be  a  silly  person — for 
though  your  reading  my  book  is  rather  a  contrary  presumption, 


BENJAMIN   FRANKLIN.  429 

yet  it  is  not  conclusive — and  your  observations  may  be  silly 
or  irrelevant,  but  you  cannot  tell  what  use  they  may  be  of  long 
after  you  are  gone  where  Budgeteers  cease  from  troubling. 

I  picked  up  the  following  book,  printed  by  J.  Franklin  at 
Boston,  during  the  period  in  which  his  younger  brother  Benjamin 
was  his  apprentice.  And  as  Benjamin  was  apprenticed  very  early, 
and  is  recorded  as  having  learnt  the  mechanical  art  very  rapidly, 
there  is  some  presumption  that  part  of  it  may  be  his  work,  though 
he  was  but  thirteen  at  the  time.  As  this  set  of  editions  of 
Hodder  (by  Mose)  is  not  mentioned,  to  my  knowledge,  I  give  the 
title  in  full : — 

Hodder's  Arithmetick :  or  that  necessary  art  made  most  easy : 
Being  explained  in  a  way  familiar  to  the  capacity  of  any  that  desire 
to  learn  it  in  a  little  time.  By  James  Hodder,  Writing-master.  The 
Five  and  twentieth  edition,  revised,  augmented,  and  above  a  thousand 
faults  amended,  by  Henry  Mose,  late  servant  and  successor  to  the 
author.  Boston  :  printed  by  J.  Franklin,  for  S.  Phillips,  N.  Buttolph, 
B.  Elliot,  D.  Henchman,  G.  Phillips,  J.  Elliot,  and  E.  Negus,  book- 
sellers in  Boston,  and  sold  at  their  shops.  1 719. 

The  book  is  a  very  small  octavo,  the  type  and  execution  are 
creditable,  the  woodcut  at  the  beginning  is  clumsy.  It  is  a 
perfect  copy,  page  for  page,  of  the  English  editions  of  Mose's 
Hodder,  of  which  the  one  called  seventeenth  is  of  London,  1690. 
There  is  not  a  syllable  to  show  that  the  edition  above  described 
might  not  be  of  Boston  in  England.  Presumptions,  but  not  very 
strong  ones,  might  be  derived  from  the  name  of  Franklin,  and 
from  the  large  number  of  booksellers  who  combined  in  the 
undertaking.  It  chanced,  however,  that  a  former  owner  had 
made  the  following  note  in  my  copy  : — 

Wednessday,  July  ye  14,  1796,  att  ten  in  ye  forenoon  we  saild  from 
Boston,  came  too  twice,  once  in  King  Rode,  and  once  in  yc  Narrows. 
Saild  by  ye  lighthouse  in  ye  even?. 

No  ordinary  map  would  decide  these  points  :  so  I  had  to 
apply  to  my  friend  Sir  Francis  Beaufort,  and  the  charts  at  the 
Admiralty  decided  immediately  for  Massachusetts. 

The  French  are  able  paradoxers  in  their  spelling  of  foreign 
names.  The  Abbe  Sabatier  de  Castres,  in  1772,  gives  an  account 
of  an  imaginary  dialogue  between  Swif,  Adisson,  Otwai,  and 
Bolingbrocke.  I  had  hoped  that  this  was  a  thing  of  former  days, 


430  A   BUDGET   OF  PARADOXES. 

like  the  literal  roasting  of  heretics  ;  but  the  charity  which  hopeth 
all  things  must  hope  for  disappointments.  Looking  at  a  recent 
work  on  the  history  of  the  Popes,  I  found  referred  to,'  in  the 
matter  of  Urban  VIII.  and  Galileo,  references  to  the  works  of  two 
Englishmen,  the  Kev.  Win  Worewel  and  the  Eev.  Eaden  Powen. 
[Wm.  Whewell  and  Baden  Powell]. 

I  must  not  forget  the  '  moderate  computation '  paradox.  This 
is  the  way  by  which  large  figures  are  usually  obtained.  Anything 
surprisingly  great  is  got  by  the  '  lowest  computation,'  anything  as 
surprisingly  small  by  the  '  utmost  computation ' ;  and  these  are 
the  two  great  subdivisions  of  '  moderate  computation.'  In  this 
way  we  learn  that  70,000  persons  were  executed  in  one  reign,  and 
150,000  persons  burned  for  witchcraft  in  one  century.  Some- 
times this  computation  is  very  close.  By  a  card  before  me  it 
appears  that  all  the  Christians,  including  those  dispersed  in 
heathen  countries,  those  of  Great  Britain  and  Ireland  excepted, 
are  198,728,000  people,  and  pay  their  clergy  8,852,OOOZ.  But 
6,400,000  people  pay  the  clergy  of  the  Anglo-Irish  Establishment 
8,896,000^. ;  and  14,600,000  of  other  denominations  pay 
1 ,024,000^  When  I  read  moderate  computations,  I  always  think 
of  Voltaire  and  the  '  memoires  du  fameux  eveque  de  Chiapa,  par 
lesquels  il  parait  qu'il  avait  egorge,  ou  brule,  ou  noye  dix  millions 
d'infideles  en  Amerique  pour  les  convertir.  Je  crus  que  cet 
eveque  exaggerait ;  mais  quaud  on  reduisait  ces  sacrifices  a  cinq 
millions  de  victimes,  cela  serait  encore  admirable.' 

My  Budget  has  been  arranged  by  authors.  This  is  the  only 
plan,  for  much  of  the  remark  is  personal :  the  peculiarities  of  the 
paradoxer  are  a  large  part  of  the  interest  of  the  parados.  As  to 
subject-matter,  there  are  points  which  stand  strongly  out ;  the 
quadrature  of  the  circle,  for  instance.  But  there  are  others 
which  cannot  be  drawn  out  so  as  to  be  conspicuous  in  a  review 
of  writers :  as  one  instance,  I  may  take  the  centrifugal  force. 

When  I  was  about  nine  years  old  I  was  taken  to  hear  a  course 
of  lectures,  given  by  an  itinerant  lecturer  in  a  country  town,  to 
get  as  much  as  I  could  of  the  second  half  of  a  good,  sound,  philo- 
sophical omniscience.  The  first  half  (and  sometimes  more)  comes 
by  nature.  To  this  end  I  smelt  chemicals,  learned  that  they  were 
different  kinds  of  gin,  saw  young  wags  try  to  kiss  the  girls  under 
the  excuse  of  what  was  called  laughing  gas — which  I  was  sure 
was  not  to  blame  for  more  than  five  per  cent,  of  the  requisite 
assurance — and  so  forth.  This  was  all  well  so  far  as  it  went ;  but 
there  was  also  the  excessive  notion  of  creative  power  exhibited  in 
the  millions  of  miles  of  the  solar  system,  of  which  power  I  won- 


AN   ITINERANT   LECTURER — CAMBRIDGE   POETS.  431 

dered  they  did  not  give  a  still  grander  idea  by  expressing  the 
distances  in  inches.  But  even  this  was  nothing  to  the  ingenious 
contrivance  of  the  centrifugal  force.  '  You  have  heard  what  I 
have  said  of  the  wonderful  centripetal  force,  by  which  Divine 
Wisdom  has  retained  the  planets  in  their  orbits  round  the  Sun. 
But,  ladies  and  gentlemen,  it  must  be  clear  to  you  that  if  there 
were  no  other  force  in  action,  this  centripetal  force  would  draw 
our  earth  and  the  other  planets  into  the  Sun,  and  universal  ruin 
would  ensue.  To  prevent  such  a  catastrophe,  the  same  wisdom 
has  implanted  a  centrifugal  force  of  the  same  amount,  and 
directly  opposite,'  &c.  I  had  never  heard  of  Alfonso  X.  of  Castile, 
but  I  ventured  to  think  that  if  Divine  Wisdom  had  just  let  the 
planets  alone  it  would  come  to  the  same  thing,  with  equal  and 
opposite  troubles  saved.  The  paradoxers  deal  largely  in  specu- 
lation conducted  upon  the  above  explanation.  They  provide 
external  agents  for  what  they  call  the  centrifugal  force.  Some 
make  the  sun's  rays  keep  the  planets  off,  without  a  thought  about 
what  would  become  of  our  poor  eyes  if  the  push  of  the  light  which 
falls  on  the  earth  were  a  counterpoise  to  all  its  gravitation.  The 
true  explanation  cannot  be  given  here,  for  want  of  room. 

Sometimes  a  person  who  has  a  point  to  carry  will  assert  a 
singular  fact  or  prediction  for  the  sake  of  his  point ;  and  this 
paradox  has  almost  obtained  the  sole  use  of  the  name.  Persons 
who  have  reputation  to  care  for  should  beware  how  they  adopt 
this  plan,  which  now  and  then  eventuates  a  spanker,  as  the 
American  editor  said.  Lord  Byron,  in  '  English  Bards,  &c..' 
(1809)  ridiculing  Cambridge  poetry,  wrote  as  follows  : — 

But  where  fair  Isis  rolls  her  purer  wave, 

The  partial  muse  delighted  loves  to  lave  ; 

On  her  green  banks  a  greener  wreath  she  wove, 

To  crown  the  bards  that  haunt  her  classic  grove  ; 

Where  Richards  wakes  a  genuine  poet's  tires, 

And  modern  Britons  glory  in  their  sires.1 

There  is  some  account -of  the  Kev.  Geo.  Richards,  Fellow  of  Oriel 
and  Vicar  of  Bampton,  (M.A.  in  1791)  in  the  'Living  Authors,' 
byWatkinsand  Shoberl  (1816).  In  Rivers's  'Living  Authors,'  of 
1798,  which  is  best  fitted  for  citation,  as  being  published  before 
Lord  Byron  wrote,  he  is  spoken  of  in  high  terms.  The  '  Abo- 
riginal Britons'  was  an  Oxford  (special)  prize  poem,  of  1791. 
Charles  Lamb  mentions  Richards  as  his  school-fellow  at  Christ's 

1  The  '  Aboriginal  Britons,'  an  excellent  poem,  by  Richards.     (Note  by  Byron.) 


432  A   BUDOET   OF  PARADOXES. 

Hospital, '  author  of  the  "  Aboriginal  Britons,"  the  most  spirited 
of  the  Oxford  Prize  Poems  :  a  pale,  studious  Grecian.' 

As  I  never  heard  of  Kichards  as  a  poet,  I  conclude  that  his 
fame  is  defunct,  except  in  what  may  prove  to  be  a  very  ambiguous 
kind  of  immortality,  conferred  by  Lord  Byron.  The  awkwardness 
of  a  case' which  time  has  broken  down  is  increased  by  the  eulogist 
himself  adding  so  powerful  a  name  to  the  list  of  Cambridge  poets, 
that  his  college  has  placed  his  statue  in  the  library,  more  con- 
spicuously than  that  of  Newton  in  the  chapel ;  and  this  although 
the  greatness  of  poetic  fame  had  some  serious  drawbacks  in  the 
moral  character  of  some  of  his  writings.  And  it  will  be  found  on 
inquiry  that  Byron,  to  get  his  instance  against  Cambridge,  had 
to  go  back  eighteen  years,  passing  over  seven  intermediate  pro- 
ductions, of  which  he  had  either  never  heard,  or  which  he  would 
not  cite  as  waking  a  genuine  poet's  fires. 

The  conclusion  seems  to  be  that  the  '  Aboriginal  Britons '  is 
a  remarkable  youthful  production,  not  equalled  by  subsequent 
efforts. 

To  enhance  the  position  in  which  the  satirist  placed  himself, 
two  things  should  be  remembered.  First,  the  glowing  and 
justifiable  terms  in  which  Byron  had  spoken, — a  hundred  and 
odd  lines  before  he  found  it  convenient  to  say  no  Cambridge 
poet  could  compare  with  Richards, — of  a  Cambridge  poet  who 
died  only  three  years  before  Byron  wrote,  and  produced  greatly 
admired  works  while  actually  studying  in  the  University.  The 
fame  of  Kirke  White  still  lives ;  and  future  literary  critics  may 
perhaps  compare  his  writings  and  those  of  Richards,  simply  by 
reason  of  the  curious  relation  in  which  they  are  here  placed 
alongside  of  each  other.  And  it  is  much  to  Byron's  credit  that, 
in  speaking  of  the  deceased  Cambridge  poet,  he  forgot  his  own 
argument  and  its  exigencies,  and  proved  himself  only  a  paradoxer 
pro  re  nata. 

Secondly,  Byron  was  very  unfortunate  in  another  passage  of  the 
same  poem : — 

What  varied  wonders  tempt  us  as  they  pass  ! 
The  cow-pox,  tractors,  galvanism,  and  gas. 
In  turns  appear,  to  make  the  vulgar  stare, 
Till  the  swoln  bubble  bursts — and  all  is  air  ! 

Three  of  the  bubbles  have  burst  to  mighty  ends.  The  metallic 
tractors  are  disused ;  but  the  force  which,  if  anything,  they  put 
in  action,  is  at  this  day,  under  the  name  of  mesmerism,  used,  pro- 


FALSIFIED   PREDICTION.  433 

hibited,  respected,  scorned,  assailed,  defended,  asserted,  denied, 
declared  utterly  obscure,  and  universally  known.  It  was  bard 
lines  to  select  four  candidates  for  oblivion  not  one  of  wbom  got 
in.  I  shall  myself,  I  am  assured,  be  some  day  cited  for  laughing 

at  the  great  discovery  of :  the  blank  is  left  for  my  reader  to 

fill  up  in  his  own  way ;  but  I  think  I  shall  not  be  so  unlucky  in 
four  different  ways. 

The  narration  before  the  fact,  as  prophecy  has  been  called, 
sometimes  quite  as  true  as  the  narration  after  the  fact,  is  very 
ridiculous  when  it  is  wrong.  Why,  the  pre-narrator  could  not 
know ;  the  post-narrator  might  have  known.  A  good  collection 
of  unlucky  predictions  might  be  made  :  I  hardly  know  one  so  fit 
to  go  with  Byron's  as  that  of  the  Eev.  Daniel  Rivers,  already 
quoted,  about  Johnson's  biographers.  Peter  Pindar  may  be 
excused,  as  personal  satire  was  his  object,  for  addressing  Boswell 
and  Mrs.  Piozzi  as  follows  : — 

Instead  of  adding  splendour  to  his  name, 
Your  books  are  downright  gibbets  to  his  fame  ; 
You  never  with  posterity  can  thrive, 
"Pis  by  the  Rambler's  death  alone  you  live. 

But  Rivers,  in  prose  narrative,  was  not  so  excusable.  He  says  : — 
'  As  admirers  of  the  learning  and  moral  excellence  of  their  hero, 
we  glow  at  almost  every  page  with  indignation  that  his  weak- 
nesses and  his  failings  should  be  disclosed  to  public  view  .  .  . 
Johnson,  after  the  lustre  he  had  reflected  on  the  name  of  Thrale 
.  .  .  was  to  have  his  memory  tortured  and  abused  by  her  detested 
itch  for  scribbling.  More  injury,  we  will  venture  to  affirm,  has 
been  done  to  the  fame  of  Johnson  by  this  Lady  and  her  late 
biographical  helpmate,  than  his  most  avowed  enemies  have  been 
able  to  effect :  and  if  his  character  becomes  unpopular  with  some 
of  his  successors,  it  is  to  those  gossiping  friends  he  is  indebted  for 
the  favour.' 

Poor  dear  old  Sam !  the  best  known  dead  man  alive !  clever, 
good-hearted,  logical,  ugly  bear  !  Where  would  he  have  been 
if  it  had  not  been  for  Boswell  and  Thrale>  and  their  imitators  ? 
What  would  biography  have  been  if  Boswell  had  not  shown  how 
to  write  a  life  ? 

Rivers  is  to  be  commended  for  not  throwing  a  single  stone  at 
Mrs.  Thrale's  second  marriage.  This  poor  lady  begins  to  receive 
a  little  justice.  The  literary  world  seems  to  have  found  out  that 
a  blue-stocking  dame  who  keeps  open  house  for  a  set  among 
them  has  a  light,  if  it  so  please  her,  to  marry  again  without 

i  i 


434  A   BUDGET   OF  PAEADOXES. 

taking  measures  to  carry  on  the  cake-shop.  I  was  before  my  age 
in  this  respect  :  as  a  boy-reader  of  Boswell,  and  a  few  other 
things  that  fell  in  my  way,  I  came  to  a  clearness  that  the  conduct 
of  society  towards  Mrs.  Piozzi  was  blackguard.  She  wanted 
nothing  but  what  was  in  that  day  a  woman's  only  efficient  protec- 
tion, a  male  relation  with  a  brace  of  pistols,  and  a  competent 
notion  of  using  them. 

Byron's  mistake  about  Hallam  in  the  Pindar  story  may  be 
worth  placing  among  absurdities.  For  elucidation,  suppose  that 
some  poet  were  now  to  speak  — 

Of  man's  first  disobedience,  and  the  fruit 
Eve  gave  to  Adam  in  his  birthday  suit  — 

and  some  critic  were  to  call  it  nonsense,  would  that  critic  be 
laughing  at  Milton  ?  Payne  Knight,  in  his  Taste,  translated  part 
of  Gray's  Bard  into  Greek.  Some  of  his  lines  are 

()'  6  riyydtv 


Literally  thus  :  — 

Wetting  warm  tears  with  groans, 
Continuous  chant  with  fearful 
Voice  he  sang. 

On  which  Hallam  remarks  :  '  The  twelfth  line  [our  first]  is 
nonsense.'  And  so  it  is,  a  poet  can  no  more  wet  his  tears  with 
his  groans  than  wet  his  ale  with  his  whistle.  Now  this  first  line 
is  from  Pindar,  but  is  only  part  of  the  sense  ;  in  full  it  is  :  — 


opSiov  fywvaae. 

Pindar's  rfyywv  must  be  Englished  by  shedding,  and  he  stands 
alone  in  this  use.  He  says,  '  shedding  warm  tears,  he  cried  out 
loud,  with  groans.'  Byron  speaks  of  — 

Classic  Hallam,  much  renowned  for  Greek  : 

and  represents  him  as  criticising  the  Greek  of  all  Payne's  lines, 
and  not  discovering  that  '  the  lines  '  were  Pindar's  until  afteJ 
publication.  Byron  was  too  much  of  a  scholar  to  make  this 


BYRON   AND   WORDSWORTH.  435 

blunder  himself:  he  either  accepted  the  facts  from  report,  or  else 
took  satirical  licence.  And  why  not?  If  you  want  to  laugh  at 
a  person,  and  he  will  not  give  occasion,  whose  fault  is  it  that  you 
are  obliged  to  make  it  ?  Hallam  did  criticise  some  of  Payne 
Knight's  Greek  ;  but  with  the  caution  of  his  character,  he  remarked 
that  possibly  some  of  these  queer  phrases  might  be  '  critic-traps ' 
justified  by  some  one  use  of  some  one  author.  I  remember  well 
having  a  Latin  essay  to  write  at  Cambridge,  in  which  I  took  care 
to  insert  a  few  monstrous  and  unusual  idioms  from  Cicero  :  a 
person  with  a  Nizolius,  and  without  scruples  may  get  scores  of 
them.  So  when  my  tutor  raised  his  voice  against  these  oddities, 
I  was  up  to  him,  for  I  came  down  upon  him  with  Cicero,  chapter 
and  verse,  and  got  round  him.  And  so  my  own  solecisms,  many 
of  them,  passed  unchallenged. 

Byron  had  more  good  in  his  nature  than  he  was  fond  of  letting 
out :  whether  he  was  a  soured  misanthrope,  or  whether  his  vein 
lay  that  way  in  poetry,  and  he  felt  it  necessary  to  fit  his  demeanour 
to  it,  are  matters  far  beyond  me.  Mr.  Crabb  Eobinson  told  me 
the  following  story  more  than  once.  He  was  at  Charles  Lamb's 
chambers  in  the  Temple  when  Wordsworth  came  in,  with  the  new 
Edinburgh  Review  in  his  hand,  and  fume  on  his  countenance. 
'  These  reviewers,'  said  he,  '  put  me  out  of  patience  !  Here  is  a 
young  man — they  say  he  is  a  lord — who  has  written  a  volume  of 
poetry  ;  and  these  fellows,  just  because  he  is  a  lord,  set  upon  him, 
laugh  at  him,  and  sneer  at  his  writing.  The  young  man  will  do 
something,  if  he  goes  on  as  he  has  begun.  But  these  reviewers 
seem  to  think  that  nobody  may  write  poetry,  unless  he  lives  in  a 
garret.'  Crabb  Eobinson  told  this  long  after  to  Lady  Byron,  who 
said,  '  Ah  !  if  Byron  had  known  that,  he  would  never  have  attacked 
Wordsworth.  He  went  one  day  to  meet  Wordsworth  at  dinner  ; 
when  he  came  home  I  said,  "  Well,  how  did  the  young  poet  get 
on  with  the  old  one  ?  "  "  Why,  to  tell  you  the  truth,"  said  he, "  I 
had  but  one  feeling  from  the  beginning  of  the  visit  to  the  end? 
and  that  was — reverence ! '"  Lady  Byron  told  my  wife  that  her 
husband  had  a  very  great  respect  for  Wordsworth.  I  suppose 
he  would  have  said — as  the  Archangel  said  to  his  Satan — '  Our 
difference  is  po[li  =  e]tical.' 

I  suspect  that  Fielding  would,  if  all  were  known,  be  ranked 
among  unlucky  railers  at  supposed  paradox.  In  his  '  Miscellanies' 
(1742,  8vo.)  he  wrote  a  satire  on  the  Chrysippus  or  Guinea,  an 
animal  which  multiplies  itself  by  division,  like  the  polypus.  This 
he  supposes  to  have  been  drawn  up  by  Petru?  Gualterus,  meaning 
the  famous  usurer,  Peter  Walter.  He  calls  it  a  paper  '  proper  to 


436  A  BUDGET   OF  PAKADOXES. 

be  read  before  the  R — 1  Society' ;  and  next  year  1743,  a  quarto 
reprint  was  made  to  resemble  a  paper  in  the  Philosophical 
Transactions.  So  far  as  I  can  make  out,  one  object  is  ridicule  of 
what  the  zoologists  said  about  the  polypus  :  a  reprint  in  the  form 
of  the  Transactions  was  certainly  satire  on  the  Society,  not  on 
Peter  "Walter  and  his  knack  of  multiplying  guineas. 

Old  poets  have  recognised  the  quadrature  of  the  circle  as  a  well- 
known  difficulty.  Dante  compares  himself,  when  bewildered,  to 
a  geometer  who  cannot  find  the  principle  on  which  the  circle  is  to 
be  measured : — 

Quale  e  '1  geometra  che  tutto  s'  affige 
Per  misurar  lo  cerchio,  e  non  ritruova, 
Pensando  qual  principio  ond'  egli  indige. 

And  Quarles  speaks  as  follows  of  the  summum  bonum  : — 

Or  ia  't  a  tart  idea,  to  procure 

An  edge,  and  keep  the  practic  soul  in  ure, 

Like  that  dear  chymic  dust,  or  puzzling  quadrature  ? 

The  poetic  notion  of  the  quadrature  must  not  be  forgotten. 
Aristophanes,  in  the  Birds,  introduces  a  geometer  who  announces 
his  intention  to  make  a  square  circle.  Pope,  in  the  Dunciad, 
delivers  himself  as  follows,  with  a  Greek  pronunciation  rather 
strange  in  a  translator  of  Homer.  Probably  Pope  recognised,  as 
a  general  rule,  the  very  common  practice  of  throwing  back  the 
accent  in  defiance  of  quantity,  seen  in  o'rator,  au'ditor,  se'nator, 
ca'tenary,  &c. — 

Mad  Mathesis  alone  was  unconfined, 
Too  mad  for  mere  material  chains  to  bind, — 
Now  to  pure  space  lifts  her  ecstatic  stare, 
Now,  running  round  the  circle,  finds  it  square. 

The  author's  note  explains  that  this  f  regards  the  wild  and  fruitless 
attempts  of  squaring  the  circle.'  The  poetic  idea  seems  to  be 
that  the  geometers  try  to  make  a  square  circle.  Disraeli  quotes 
it  as  '  finds  its  square,'  but  the  originals  do  not  support  this 
reading. 

I  have  come  in  the  way  of  a  work,  entitled  '  The  Grave  of 
Human  Philosophies,'  (1827)  translated  from  the  French  of  R.  de 
Becourt  by  A.  Dalmas.  It  supports,  but  I  suspect  not  very 
accurately,  the  views  of  the  old  Hindoo  books.  That  the  sun  is 


DE  BE"COURT.— BEQUEST  OF  A  QUADRATURE.        437 

only  450  miles  from  us,  and  only  40  miles  in  diameter,  may  be 
passed  over ;  my  affair  is  with  the  state  of  mind  into  which 
persons  of  M.  Becourt's  temperament  are  brought  by  a  fancy. 
He  fully  grants,  as  certain,  four  millions  of  years  as  the  duration 
of  the  Hindoo  race,  and  1956  as  that  of  the  universe.  It  must  be 
admitted  he  is  not  wholly  wrong  in  saying  that  our  errors  about 
the  universe  proceed  from  our  ignorance  of  its  origin,  antiquity, 
organization,  laws,  and  final  destination.  Living  in  an  age  of 
light,  he  *  avails  himself  of  that  opportunity '  to  remove  this  veil 
of  darkness,  &c.  The  system  of  the  Brahmins  is  the  only  true 
one :  he  adds  that  it  has  never  before  been  attempted,  as  it  could 
not  be  obtained  except  by  him.  The  author  requests  us  first,  to 
lay  aside  prejudice  ;  next,  to  read  all  he  says  in  the  order  in 
which  he  says  it :  we  may  then  pronounce  judgment  upon  a  work 
which  begins  by  taking  the  Brahmins  for  granted.  All  the 
paradoxers  make  the  same  requests.  They  do  not  see  that  com- 
pliance would  bring  thousands  of  systems  before  the  world  every 
year  :  we  have  scores  as  it  is.  How  is  a  poor  candid  inquirer  to 
choose  Fortunately,  the  mind  has  its  grand  jury  as  well  as  its 
little  one  :  and  it  will  not  put  a  book  upon  its  trial  without  a 
primd  facie  case  in  its  favour.  And  with  most  of  those  who 
really  search  for  themselves,  that  case  is  never  made  out  without 
evidence  of  knowledge,  standing  out  clear  and  strong,  in  the  book 
to  be  examined. 

There  is  much  private  history  which  will  never  come  to  light, 
caret  quia  vote  sacro,  because  no  Budgeteer  comes  across  it. 
Many  years  ago  a  man  of  business,  whose  life  was  passed  in 
banking,  amused  his  leisure  with  quadrature,  was  successful  of 
course,  and  bequeathed  the  result  in  a  sealed  book,  which  the 
legatee  was  enjoined  not  to  sell  under  a  thousand  pounds.  The 
true  ratio  was  3*1416  :  I  have  the  anecdote  from  the  legatee's 
executor,  who  opened  the  book.  That  a  banker  should  square  the 
circle  is  very  credible :  but  how  could  a  City  man  come  by  the  notion 
that  a  thousand  pounds  could  be  got  for  it  ?  A  friend  of  mine, 
one  of  the  twins  of  my  zodiac,  will  spend  a  thousand  pounds,  if 
he  have  not  done  it  already,  in  black  and  white  cyclometry :  but 
I  will  answer  for  it  that  he,  a  man  of  sound  business  notions, 
never  entertained  the  idea  of  TT  recouping  him,  as  they  now  say. 
I  speak  of  individual  success :  of  course  if  a  company  were 
formed,  especially  if  it  were  of  unlimited  lie-ability,  the  shares 
would  be  taken.  No  offence ;  there  is  nothing  but  what  a  pun 
will  either  sanctify,  justify,  or  nullify  : — 

It  comes  o'er  the  soul  like  the  sweet  South 
That  breathes  upon  a  bank  of  vile  hits. 


438  A   BUDGET   OF  PARADOXES. 

The  shares  would  be  at  a  premium  of  3^  on  the  day  after  issue. 
If  they  presented  me  with  the  number  of  shares  I  deserve,  for 
suggestion  and  advertisement,  I  should  stand  up  for  the  Arch- 
priest  of  St.  Vitus  and  3^-,  with  a  view  to  a  little  more  gold  on 
the  bridge. 

I  now  insert  a  couple  of  reviews,  one  about  Cyclopaedias,  one 
about  epistolary  collections.  Should  any  reader  wish  for  expla- 
nation of  this  insertion,  I  ask  him  to  reflect  a  moment,  and 
imagine  me  set  to  justify  all  the  additions  now  before  him  !  In 
truth  these  reviews  are  the  repositories  of  many  odds  and  ends  : 
they  were  not  made  to  the  books ;  the  materials  were  in  my  notes, 
and  the  books  came  as  to  a  ready-made  clothes  shop,  and  found 
what  would  fit  them.  Many  remember  Curll's  bequest  of  some 
very  good  titles  which  only  wanted  treatises  written  to  them. 
Well !  here  were  some  tolerable  reviews — as  times  go — which 
only  wanted  books  fitted  to  them.  Accordingly,  some  tags  were 
made  to  join  on  the  books  ;  and  then  as  the  reader  sees. 

I  should  find  it  hard  to  explain  why  the  insertion  is  made 
in  this  place  rather  than  another.  But  again,  suppose  I  were 
put  to  make  such  an  explanation  throughout  the  volume.  The 
improver  who  laid  out  grounds  and  always  studied  what  he  called 
unexpectedness,  was  asked  what  name  he  gave  it  for  those  who 
walked  over  his  grounds  a  second  time.  He  was  silenced ;  but  I 
have  an  answer  :  It  is  that  which  is  given  by  the  very  procedure 
of  taking  up  my  book  a  second  time. 


October  19, 1861.    The  English  Cyclopcedia.    Conducted  by  Charles 

Knight.    22  vols. :  viz.,  Geography,  4  vols. ;  Biography,  6  vols. ; 

Natural  History,  4  vols. ;  Arts  and  Sciences,  8  vols.     (Bradbury 

&  Evans.) 
The  Encyclopaedia  Britannica  :  a  Dictionary  of  Arts,  Sciences,  and 

General  Literature.      Eighth    Edition.      21   vols.   and   Index. 

(Black.) 

The  two  editions  above  described  are  completed  at  the  same 
time :  and  they  stand  at  the  head  of  the  two  great  branches  into 
which  pantological  undertakings  are  divided,  as  at  once  the  largest 
and  the  best  of  their  classes. 

When  the  works  are  brought  together,  the  first  thing  that 
strikes  the  eye  is  the  syllable  of  difference  in  the  names.  The 
word  Cydopaidia  is  a  bit  of  modern  purism.  Though  eyicvtcXo- 
is  not  absolutely  Greek  of  Greece,  we  learn  from  both 


REVIEW   OF   CYCLOPEDIAS.  439 

Pliny  and  Quintilian  that  the  circle  of  the  sciences  was  so  called 
by  the  Greeks,  and  Vitruvius  has  thence  naturalized  encyclium  in 
Latin.  Nevertheless  we  admit  that  the  initial  en  would  have 
euphonized  but  badly  with  the  word  Penny :  and  the  English 
Cyclopaedia  is  the  augmented,  revised,  and  distributed  edition  of 
the  Penny  Cyclopaedia.  It  has  indeed  been  said  that  Cyclopedia 
should  mean  the  education  of  a  circle,  just  as  Cyropaedia  is  the 
education  of  Cyrus.  But  this  is  easily  upset  by  Aristotle's  word 
KUK\o(f>opla,  motion  in  a  circle,  and  by  many  other  cases,  for 
which  see  the  lexicon. 

The  earliest  printed  Encyclopedia  of  this  kind  was  perhaps 
the  famous  '  myrrour  of  the  worlde,'  which  Caxton  translated 
from  the  French  and  printed  in  1480.  The  original  Latin  is  of 
the  thirteenth  century,  or  earlier.  This  is  a  collection  of  very 
short  treatises.  In  or  shortly  after  1496  appeared  the  'Margarita 
Philosophica '  of  Gregory  Keisch,  the  same  we  must  suppose,  who 
was  confessor  to  the  Emperor  Maximilian.  This  is  again  a  col- 
lection of  treatises,  of  much  more  pretension  :  and  the  estimation 
formed  of  it  is  proved  by  the  number  of  editions  it  went  through. 
In  1531,  appeared  the  little  collection  of  works  of  Ringelberg, 
which  is  truly  called  an  Encyclopaedia  by  Morhof,  though  the 
thumbs  and  fingers  of  the  two  hands  will  meet  over  the  length  of 
its  one  volume.  There  are  more  small  collections ;  but  we  pass 
on  to  the  first  work  to  which  the  name  of  Encyclopaedia  is  given. 
This  is  a  ponderous  '  Scientiarum  Omnium  Encyclopaedia '  of 
Alsted,  in  four  folio  volumes,  commonly  bound  in  two  ;  published 
in  1629  and  again  in  1649  ;  the  true  parent  of  all  the  Encyclo- 
paedias, or  collections  of  treatises,  or  works  in  which  that  character 
predominates.  The  first  great  dictionai*y  may  perhaps  be  taken 
to  be  Hofman's  'Lexicon  Universale '  (1677);  but  Chambers's 
(so  called)  Dictionary  (1728)  has  a  better  claim.  And  we  support 
our  proposed  nomenclature  by  observing  that  Alsted  accidentally 
called  his  work  Encyclopaedia,  and  Chambers  simply  Cyclo- 
paedia. 

We  shall  make  one  little  extract  from  the  '  myrrour,'  and  one 
from  Ringelberg.  Caxton's  author  makes  a  singular  remark  for 
his  time  ;  and  one  well  worthy  of  attention.  The  grammar  rules 
of  a  language,  he  says,  must  have  been  invented  by  foreigners : 
'  And  whan  any  suche  tonge  was  perfytely  had  and  usyd  amonge 
any  people,  than  other  people  not  used  to  the  same  tonge  caused 
rulys  to  be  made  wherby  they  myght  lerne  the  same  tonge  .... 
and  suche  rulys  be  called  the  gramer  of  that  tonge.'  Ringelberg 
says  that  if  the  right  nostril  bleed,  the  little  finger  of  the  right 


440  A   I3UDGET   OF  PARADOXES. 

hand  should  be  crooked,  and  squeezed  with  great  force  ;  and  the 
same  for  the  left. 

We  pass  on  to  the  Encyclopedic,  commenced  in  1751 ;  the  work 
which  has,  in  many  minds,  connected  the  word  encyclopedist  with 
that  of  infidel.  Headers  of  our  day  are  surprised  when  they  look 
into  this  work,  and  wonder  what  has  become  of  all  the  irreligion. 
The  truth  is,  that  the  work — though  denounced  ab  ovo  on  account 
of  the  character  of  its  supporters — was  neither  adapted,  nor  in- 
tended, to  excite  any  particular  remark  on  the  subject :  no  work 
of  which  D'Alembert  was  co-editor  would  have  been  started  on 
any  such  plan.  For,  first,  he  was  a  real  sceptic  :  that  is,  doubtful, 
with  a  mind  not  made  up.  Next,  he  valued  his  quiet  more  than 
anything ;  and  would  as  soon  have  gone  to  sleep  over  an  hornet's 
nest  as  have  contemplated  a  systematic  attack  upon  either  religion 
or  government.  As  to  Diderot — of  whose  varied  career  of  thought 
it  is  difficult  to  fix  the  character  of  any  one  moment,  but  who  is 
very  frequently  taken  among  us  for  a  pure  atheist — we  will  quote 
one  sentence  from  the  article  '  Encyclopedic,'  which  he  wrote 
himself: — 'Dans  le  moral,  il  n'y  a  que  Dieu  qui  doit  servir  de 
modele  a  1'homme ;  dans  les  arts,  que  la  nature.' 

A  great  many  readers  in  our  country  have  but  a  very  hazy  idea 
of  the  difference  between  the  political  Encyclopaedia,  as  we  may 
call  it,  and  the  Encyclopedic  Methodique,  which  we  always  take 
to  be  meant  —whether  rightly  or  not  we  cannot  tell — when  we 
hear  of  the  '  great  French  Encyclopaedia.'  This  work,  which  takes 
much  from  its  predecessor,  professing  to  correct  it,  was  begun  in 
1792,  and  finished  in  1832.  There  are  166  volumes  of  text,  and 
6,439  plates,  which  are  sometimes  incorporated  with  the  text, 
sometimes  make  about  40  more  volumes.  This  is  still  the  monster 
production  of  the  kind  ;  though  probably  the  German  Cyclopaedia 
of  Ersch  and  Grruber,  which  was  begun  in  1818,  and  is  still  in 
progress,  will  beat  it  in  size.  The  great  French  work  is  a  collec- 
tion of  dictionaries  ;  it  consists  of  Cyclopaedias  of  all  the  separate 
branches  of  knowledge.  It  is  not  a  work,  but  a  collection  of  works, 
one  or  another  department  is  to  be  bought  from  time  to  time ; 
but  we  never  heard  of  a  complete  set  for  sale  in  one  lot.  As  ships 
grow  longer  and  longer,  the  question  arises  what  limit  there  is  to 
the  length.  One  answer  is,  that  it  will  never  do  to  try  such  a 
length  that  the  stern  will  be  rotten  before  the  prow  is  finished. 
This  wholesome  rule  has  not  been  attended  to  in  the  matter 
before  us ;  the  earlier  parts  of  the  great  French  work  were 
antiquated  before  the  whole  were  completed  :  something  of  the 
kind  will  happen  to  that  of  Ersch  and  Gruber. 


KEVIEW   OF  CYCLOPEDIAS.  441 

The  production  of  a  great  dictionary  of  either  of  the  kinds  is 
far  from  an  easy  task.     There  is  one  way  of  managing  the  En~ 
cyclopaedia  which  has  been  largely  resorted  to  ;  indeed,  we  may 
say  that  no  such  work  has  been  free  from  it.     This  plan  is  to 
throw  all  the  attention  upon  the  great  treatises,  and  to  resort  to 
paste  and  scissors,  or  some  process  of  equally  easy  character,  for 
the  smaller  articles.     However  it  may  be  done,  it  has  been  the 
rule  that  the   Encyclopaedia  of  treatises  should  have  its  supple- 
mental Dictionary  of  a  very  incomplete  character.     It  is  true  that 
the  treatises  are  intended  to  do  a  good  deal ;  and  that  the  Index, 
if  it  be  good,  knits  the  treatises  and  the  dictionary  into  one  whole 
of  reference.     Still  there  are  two  stools,  and  between  them  a  great 
deal  will   fall  to  the  ground.     The   dictionary   portion   of  the 
Britannica  is  not  to  be  compared  with  its  treatises  ;  the  part  called 
Miscellaneous  and  Lexicographical  in  the  Metropolitana  is  a  great 
failure.     The  defect  is  incompleteness.     The  biographical  portion, 
for  example,  of  the  Britannica  is  very  defective :  of  many  names 
of  note  in  literature  and  science,  which  become  known  to  the 
reader  from  the  treatises,  there  is  no  account  whatever  in  the 
dictionary.     So  that  the  reader  who  has  learnt  the  results  of  a  life 
in  astronomy,  for  example,  must  go  to  some  other  work  to  know 
when  that  life  began  and  ended.     This  defect  has  run  through  all 
the  editions  ;  it  is  in  the  casting  of  the  work.     The  reader  must 
learn  to  take  the  results  at  their  true  value,  which  is  not  small. 
He  must  accustom  himself  to  regard  the  Britannica  as  a  splendid 
body  of  treatises  on  all  that  can  be  called  heads  of  knowledge, 
both  greater  and  smaller ;  with   help    from   the    accompanying 
dictionary,  but  not  of  the  most  complete  character.     Practically, 
we  believe,  this  defect  cannot  be  avoided :  two  plans  of  essentially 
different  structure  cannot  be  associated  on  the  condition  of  each 
or  either  being  allowed  to  abbreviate  the  other. 

The  defect  of  all  others  which  it  is  most  difficult  to  avoid  is 
inequality  of  performance.  Take  any  dictionary  you  please,  of 
any  kind  which  requires  the  association  of  a  number  of  con- 
tributors, and  this  defect  must  result.  We  do  not  merely  mean 
that  some  will  do  their  work  better  than  others ;  this  of  course : 
we  mean  that  there  will  be  structural  differences  of  execution, 
affecting  the  relative  extent  of  the  different  parts  of  the  whole,  as 
well  as  every  other  point  by  which  a  work  can  be  judged.  A  wise 
editor  will  not  attempt  any  strong  measures  of  correction  :  he 
will  remember  that  if  some  portions  be  below  the  rest,  which  is  a 
disadvantage,  it  follows  that  some  portions  must  be  above  the 
rest,  which  is  an  advantage.  The  only  practical  level,  if  level 


442  A   BUDGET   OF  PARADOXES. 

there  must  be,  is  that  of  mediocrity,  if  not  of  absolute  worthless- 
ness  :  any  attempt  to  secure  equality  of  strength  will  result  in 
equality  of  weakness.  Efficient  development  may  be  cut  down 
into  meagre  brevity,  and  in  this  way  only  can  apparent  equality 
of  plan  be  secured  throughout.  It  is  far  preferable  to  count  upon 
differences  of  execution,  and  to  proceed  upon  the  acknowledged 
expectation  that  the  prominent  merits  of  the  work  will  be  settled 
by  the  accidental  character  of  the  contributors  ;  it  being  held  im- 
possible that  any  editorial  efforts  can  secure  a  uniform  standard 
of  goodness.  Wherever  the  greatest  power  is  found,  it  should  be 
suffered  to  produce  its  natural  effect.  There  are,  indeed,  critics 
who  think  that  the  merit  of  a  book,  like  the  strength  of  a  chain, 
is  that  of  its  weakest  part :  but  there  are  others  who  know  that 
the  parallel  does  not  hold,  and  who  will  remember  that  the  union 
of  many  writers  must  show  exaggeration  of  the  inequalities  which 
almost  always  exist  in  the  production  of  one  person.  The  true 
plan  is  to  foster  all  the  good  that  can  be  got,  and  to  give  develop- 
ment in  the  directions  in  which  most  resources  are  found  :  a 
Cyclopaedia,  like  a  plant,  should  grow  towards  the  light. 

The  Penny  Cyclopaedia  had  its  share  of  this  kind  of  defect  or 
excellence,  according  to  the  way  in  which  the  measure  is  taken. 
The  circumstance  is  not  so  much  noticed  as  might  be  expected, 
and  this  because  many  a  person  is  in  the  habit  of  using  such  a 
dictionary  chiefly  with  relation  to  one  subject,  his  own;  and  more 
still  want  it  for  the  pure  dictionary  purpose,  which  does  not  go 
much  beyond  the  meaning  of  the  word.  But  the  person  of  full 
and  varied  reference  feels  the  differences  ;  and  criticism  makes 
capital  of  them.  The  Useful  Knowledge  Society  was  always 
odious  to  the  organs  of  religious  bigotry  ;  and  one  of  them,  ad- 
verting to  the  fact  that  geography  was  treated  with  great  ability, 
and  most  unusual  fullness,  in  the  Penny  Cyclopaedia,  announced 
it  by  making  it  the  sole  merit  of  the  work  that,  with  sufficient 
addition,  it  would  make  a  tolerably  good  gazetteer. 

Some  of  our  readers  may  still  have  hanging  about  them  the 
feelings  derived  from  this  old  repugnance  of  a  class  to  all  that  did 
not  associate  direct  doctrinal  teaching  of  religion  with  every 
attempt  to  communicate  knowledge.  I  will  take  one  more 
instance,  by  way  of  pointing  out  the  extent  to  which  stupidity 
can  go.  If  there  be  an  astronomical  fact  of  the  telescopic 
character  which,  next  after  Saturn's  ring  and  Jupiter's  satellites, 
was  known  to  all  the  world,  it  was  the  existence  of  multitudes  of 
double  stars,  treble  stars,  &c.  A  respectable  quarterly  of  the 
theological  cast,  which  in  mercy  we  refrain  from  naming,  was 


REVIEW-  OF   CYCLOPAEDIAS.  443 

ignorant  of  this  common  knowledge, — imagined  that  the,  mention 
of  such  systems  was  a  blunder  of  one  of  the  writers  in  the  Penny 
Cyclopaedia,  and  lashed  the  presumed  ignorance  of  the  statement 
in  the  following  words,  delivered  in  April,  1837  : — 

'We  have  forgotten  the  name  of  that  Sidrophel  who  lately  dis- 
covered that  the  fixed  stars  were  not  single  stars,  but  appear  in  the 
heavens  like  soles  at  Billingsgate,  in  pairs  ;  while  a  second  astronomer, 
under  the  influence  of  that  competition  in  trade  which  the  political 
economists  tell  us  is  so  advantageous  to  the  public,  professes  to  show 
us,  through  his  superior  telescope,  that  the  apparently  single  stars  are 
really  three.  Before  such  wondrous  mandarins  of  science,  how  con- 
tinually must  homunculi  like  ourselves  keep  in  the  background,  lest  we 
come  between  the  wind  and  their  nobility.' 

Certainly  these  little  men  ought  to  have  kept  in  the  back- 
ground ;  but  they  did  not :  and  the  growing  reputation  of  the 
work  which  they  assailed  has  chronicled  them  in  literary  history  ; 
grubs  in  amber. 

This  important  matter  of  inequality,  which  has  led  us  so  far,  is 
one  to  which  the  Encyclopaedia  is  as  subject  as  the  Cyclopaedia  ; 
but  it  is  not  so  easily  recognised  as  a  fault.  We  receive  the  first 
book  as  mainly  a  collection  of  treatises  :  we  know  their  authors, 
and  we  treat  them  as  individuals.  We  see,  for  instance,  the 
names  of  two  leading  writers  on  Optics,  Brewster  and  Herschel. 
It  would  not  at  all  surprise  us  if  either  of  these  writers  should  be 
found  criticising  the  other  by  name,  even  though  the  very  view 
opposed  should  be  contained  in  the  same  Encyclopaedia  with  the 
criticism.  And  in  like  manner,  we  should  hold  it  no  wonder  if 
we  found  some  third  writer  not  comparable  to  either  of  those  we 
have  named.  It  is  not  so  in  the  Cyclopaedia  :  here  we  do  not 
know  the  author,  except  by  inference  from  a  list  of  which  we 
never  think  while  consulting  the  work.  We  do  not  dissent  from 
this  or  that  author  :  we  blame  the  book. 

The  Encyclopaedia  Britannica  is  an  old  friend.  Though  it  holds 
a  proud  place  in  our  present  literature,  yet  the  time  was  when  it 
stood  by  itself,  more  complete  and  more  clear  than  any tldng 
which  was  to  be  found  elsewhere.  There  must  be  studious  men 
alive  in  plenty  who  remember,  when  they  were  studious  boys, 
what  a  literary  luxury  it  was  to  pass  a  few  days  in  the  house 
of  a  friend  who  had  a  copy  of  this  work.  The  present  edition  is 
a  worthy  successor  of  those  which  went  before.  The  last  three 
editions,  terminating  in  1824,  1842,  and  1861,  seem  to  show  that 
a  lunar  cycle  cannot  pass  without  an  amended  and  augmented 


444  A   BUDGET   OF  PARADOXES. 

edition.  Detailed  criticism  is  out  of  the  question  ;  but  we  may 
notice  the  effective  continuance  of  the  plan  of  giving  general 
historical  dissertations  on  the  progress  of  knowledge.  Of  some 
of  these  dissertations  we  have  had  to  take  separate  notice  ;  and 
all  will  be  referred  to  in  our  ordinary  treatment  of  current  litera- 
ture. 

The  literary  excellence  of  these  two  extensive  undertakings  is 
of  the  same  high  character.  To  many  this  will  need  justification : 
they  will  not  easily  concede  to  the  chea.pand  recent  work  a  right 
to  stand  on  the  same  shelf  with  the  old  and  tried  magazine,  newly 
replenished  with  the  best  of  everything.  Those  who  are  cognizant 
by  use  of  the  kind  of  material  which  fills  the  Penny  Cyclopcedia 
will  need  no  further  evidence :  to  others  we  shall  quote  a  very 
remarkable,  and  certainly  very  complete  testimony.  The 
Cyclopcedia  of  the  Physical  Sciences,  published  by  Dr.  Nichol  in 
1857  (noticed  by  us,  April  4),  is  one  of  the  most  original  of  our 
special  dictionaries.  The  following  is  an  extract  from  the  editor's 
preface : — 

'  When  I  assented  to  Mr.  Griffin's  proposal  that  I  should  edit  such 
a  Cyclopaedia,  I  had  it  in  my  mind  that  I  might  make  the  scissors 
eminently  effective.  Alas !  on  narrowly  examining  our  best  Cyclo- 
paedias, I  found  that  the  scissors  Lad  become  blunted  through  too  fre- 
quent and  vigorous  use.  One  great  exception  exists :  viz.  the  Penny 
Cyclopaedia  of  Charles  Knight.  The  cheapest  and  the  least  pretending, 
it  is  really  the  most  philosophical  of  our  scientific  dictionaries.  It  is 
not  made  up  of  a  series  of  treatises,  some  good  and  many  indifferent, 
but  is  a  thorough  Dictionary,  well  proportioned  and  generally  written 
by  the  best  men  of  the  time.  The  more  closely  it  is  examined,  the 
more  deeply  will  our  obligations  be  felt  to  the  intelligence  and  con- 
scientiousness of  its  projector  and  editor.' 

After  Dr.  Nichol's  candid  and  amusing  announcement  of  his 
scissorial  purpose,  it  is  but  fair  to  state  that  nothing  of  the  kind 
was  ultimately  carried  into  effect,  even  upon  the  work  in  which 
he  found  so  much  to  praise.  I  quote  this  testimony  because  it  is 
of  a  peculiar  kind. 

The  success  of  the  Penny  Magazine  led  Mr.  Charles  Knight 
in  1832,  to  propose  to  the  Useful  Knowledge  Society  a  Cyclopaedia 
in  weekly  penny  numbers.  These  two  works  stamp  the  name  of 
the  projector  on  the  literature  of  our  day  in  very  legible  characters. 
Eight  volumes  of  480  pages  each  were  contemplated ;  and  Mr. 
Long  and  Mr.  Knight  were  to  take  the  joint  management.  The 
plan  embraced  a  popular  account  of  Art  and  Science,  with  very 
brief  biographical  and  geographical  information.  The  early 


REVIEW  OF  CYCLOPAEDIAS.  445 

numbers  of  the  work  had  some  of  the  Penny  Magazine  character  : 
no  one  can  look  at  the  pictures  of  the  Abbot  and  Abbess  in  their 
robes  without  seeing  this.  By  the  time  the  second  volume  was 
completed,  it  was  clearly  seen  that  the  plan  was  working  out  its 
own  extension  :  a  great  development  of  design  was  submitted  to, 
and  Mr.  Long  became  sole  editor.  Contributors  could  not  be 
found  to  make  articles  of  the  requisite  power  in  the  assigned 
space.  One  of  them  told  us  that  when  he  heard  of  the  eight 
volumes,  happening  to  want  a  shelf  to  be  near  at  hand  for  containing 
the  work  as  it  went  on,  he  ordered  it  to  be  made  to  hold  twenty- 
five  volumes  easily.  But  the  inexorable  logic  of  facts  beat  him 
after  all :  for  the  complete  work  contained  twenty-six  volumes, 
and  two  thick  volumes  of  Supplement. 

The  penny  issue  was  brought  to  an  end  by  the  state  of  the  law, 
which  required,  in  1833,  that  the  first  and  last  page  of  everything 
sold  separately  should  contain  the  name  and  address  of  the  printer. 
The  penny  numbers  contained  this  imprint  on  the  fold  of  the 
outer  leaf :  and  qui  tarn,  informations  were  laid  against  the  agents 
in  various  towns.  It  became  necessary  to  call  in  the  stock  ;  and 
the  penny  issue  was  abandoned.  Monthly  parts  were  substituted, 
which  varied  in  bulk,  as  the  demands  of  the  plan  became  more 
urgent,  and  in  price  from  one  sixpence  to  three.  The  second 
volume  of  Supplement  appeared  in  1 846,  and  during  the  fourteen 
years  of  issue  no  one  monthly  part  was  ever  behind  its  time.  This 
result  is  mainly  due  to  the  peculiar  qualities  of  Mr.  Long,  who 
unites  the  talents  of  the  scholar  and  the  editor  in  a  degree  which 
is  altogether  unusual.  If  any  one  should  imagine  that  a  mixed 
mass  of  contributors  is  a  punctual  piece  of  machinery,  let  him 
take  to  editing  upon  that  hypothesis,  and  he  shall  see  what  he 
shall  see  and  learn  what  he  shall  learn. 

The  English  contains  about  ten  per  cent,  more  matter  than 
the  Penny  Cyclopaedia  and  its  Supplements ;  including  the  third 
supplementary  volume  of  1848,  which  we  now  mention  for  the 
first  time.  The  literary  work  of  the  two  editions  cost  within  500L 
of  50,000£. :  that  of  the  two  editions  of  the  Britannica  cost  41,OOOZ. 
But  then  it  is  to  be  remembered  that  the  Britannica  had  matter 
to  begin  upon,  which  had  been  paid  for  in  the  former  editions. 
Eoughly  speaking,  it  is  probable  that  the  authorship  of  a  page  of 
the  same  size  would  have  cost  nearly  the  same  in  one  as  in  the 
other. 

The  longest  articles  in  the  Penny  Cyclopaedia  were  '  Home '  in  98 
columns  and  c  Yorkshire  '  in  86  columns.  The  only  article  which 
can  be  called  a  treatise  is  the  Astronomer  Eoyal's  '  Gravitation,' 


446  A   BUDGET   OF  PARADOXES. 

founded  on  the  method  of  Newton  in  the  eleventh  section,  but 
carried  to  a  much  greater  extent.  In  the  English  Cyclopaedia, 
the  longest  article  of  geography  is  '  Asia,'  in  45  columns.  In 
natural  history  the  antelopes  demand  36  columns.  In  biography, 
'  Wellington  '  uses  up  42  columns,  and  his  great  military  opponent 
41  columns.  In  the  division  of  Arts  and  Sciences,  which  includes 
much  of  a  social  and  commercial  character,  the  length  of  articles 
often  depends  upon  the  state  of  the  times  with  regard  to  the 
subject.  Our  readers  would  not  hit  the  longest  article  of  this 
department  in  twenty  guesses :  it  is  '  Deaf  and  Dumb '  in  60 
columns.  As  other  specimens,  we  may  cite  Astronomy,  19 ; 
Banking,  36  ;  Blind,  24 ;  British  Museum,  35 ;  Cotton,  27  ; 
Drama,  26 ;  Gravitation,  50 ;  Libraries,  50 ;  Painting,  34 ; 
Eailways,  18;  Sculpture,  36;  Steam,  &c.,  37;  Table,  40; 
Telegraph,  30  ;  Welsh  language  and  literature,  39 ;  Wool,  21  ; 
These  are  the  long  articles  of  special  subdivisions :  the  words 
under  which  the  Encyclopaedia  gives  treatises  are  not  so  prominent. 
As  in  Algebra,  10;  Chemistry,  12;  Geometry,  8;  Logic,  14; 
Mathematics,  5  ;  Music,  9.  But  the  difference  between  the  col- 
lection of  treatises  and  the  dictionary  may  be  illustrated  thus  : — 
though  '  Mathematics '  have  only  five  columns,  '  Mathematics, 
recent  terminology  of,'  has  eight :  and  this  article  we  believe  to 
be  by  Mr.  Cayley,  who  certainly  ought  to  know  his  subject,  being 
himself  a  large  manufacturer  of  the  new  terms  which  he  explains. 
Again,  though  '  Music '  in  genere,  as  the  schoolmen  said,  has  only 
nine  columns,  '  Temperament  and  Tuning'  has  eight, and  'Chord' 
alone  has  two.  And  so  on. 

In  a  dictionary  of  this  kind  it  is  difficult  to  make  a  total  clear- 
ance of  personality :  by  which  we  mean  that  exhibition  of 
peculiar  opinion  which  is  offensive  to  taste  when  it  is  shifted  from 
the  individual  on  the  corporate  book.  The  treatise  of  the  known 
author  may,  as  we  have  said,  carry  that  author's  controversies  on 
its  own  shoulders  :  and  even  his  crotchets,  if  we  may  use  such  a 
word.  But  the  dictionary  should  not  put  itself  into  antagonism 
with  general  feeling,  nor  even  with  the  feelings  of  classes.  We 
refer  particularly  to  the  ordinary  and  editorial  teaching  of  the 
article.  If,  indeed,  the  writer,  being  at  issue  with  mankind, 
should  confess  the  difference,  and  give  abstract  of  his  full  grounds, 
the  case  is  altered :  the  editor  then,  as  it  were,  admits  a  corres- 
pondent to  a  statement  of  his  own  individual  views.  The 
dictionary  portion  of  the  Britannica  is  quite  clear  of  any  lapses 
on  this  point,  so  far  as  we  know  :  the  treatises  and  dissertations 
rest  upon  their  authors.  The  Penny  Cyclopaedia  was  all  but  clear : 


REVIEW   OF   CYCLOPEDIAS.  447 

and  great  need  was  there  that  it  should  have  been  so.  The 
Useful  Knowledge  Society,  starting  on  the  principle  of  perfect 
neutrality  in  politics  and  religion,  was  obliged  to  keep  strict  watch 
against  the  entrance  of  all  attempt  even  to  look  over  the  hedge. 
There  were  two — we  believe  only  two — instances  of  what,  we  have 
called  personality.  The  first  was  in  the  article  '  Bunyan.'  It  is 
worth  while  to  extract  all  that  is  said — in  an  article  of  thirty 
lines — about  a  writer  who  is  all  .but  universally  held  to  be  the 
greatest  master  of  allegory  that  ever  wrote  : — 

'His  works  were  collected  in  two  volumes,  folio,  1736-7:  among 
them  '  The  Pilgrim's  Progress  '  has  attained  the  greatest  notoriety. 
If  a  judgment  is  to  be  formed  of  the  merits  of  a  book  by  the  number 
of  times  it  has  been  reprinted,  and  the  many  languages  into  which  it 
has  been  translated,  no  production  in  English  literature  is  superior  to 
this  coarse  allegory.  On  a  composition  which  has  been  extolled  by 
Dr.  Johnson,  and  which  in  our  own  times  has  received  a  very  high 
critical  opinion  in  its  favour  [probably  Soutliey],  it  is  hazardous  to 
venture  a  disapproval,  and  we,  perhaps,  speak  the  opinion  of  a  small 
minority  when  we  confess  that  to  us  it  appears  to  be  mean,  jejune  and 
wearisome.' 

— If  the  unfortunate  critic  who  thus  individualized  himself  had 
been  a  sedulous  reader  of  Bunyan,  his  power  over  English  would 
not  have  been  so  jejune  as  to  have  needed  that  fearful  word. 
This  little  bit  of  criticism  excited  much  amusement  at  the  time 
of  its  publication :  but  it  was  so  thoroughly  exceptional  and 
individual  that  it  was  seldom  or  never  charged  on  the  book. 
The  second  instance  occurred  in  the  article  '  Socinians.'  It  had 
been  arranged  that  the  head- words  of  Christian  sects  should  be 
intrusted  to  members  of  the  sects  themselves,  on  the  understand- 
ing that  the  articles  should  simply  set  forth  the  accounts  which 
the  sects  themselves  give  of  their  own  doctrines.  Thus  the  article 
on  the  Koman  Church  was  written  by  Dr.  Wiseman.  But  the 
Unitarians  were  not  allowed  to  come  within  the  rule  :  as  in  other 
quarters,  they  were  treated  as  the  gypsies  of  Christianity.  Under 
the  head  '  Socinians ' — a  name  repudiated  by  themselves — an 
opponent  was  allowed  not  merely  to  state  their  alleged  doctrines 
in  his  own  way,  but  to  apply  strong  terms,  such  as  'audacious 
unfairness,'  to  some  of  their  doings.  The  protests  which  were 
made  against  this  invasion  of  the  understanding  produced,  in  due 
time,  the  article  '  Unitarians,'  written  by  one  of  that  persuasion. 
"We  need  not  say  that  these  errors  have  been  amended  in  the 
English  Cyclopaedia :  and  our  chief  purpose  in  mentioning  them 
is  to  remark,  that  this  is  all  we  can  find  on  the  points  in  question 


448  A  BUDGET   OF  PARADOXES. 

against  twenty-eight  large  volumes  produced  by  an  editor  whose 
task  was  monthly,  and  whose  issue  was  never  delayed  a  single 
hour.  How  much  was  arrested  before  publication  none  but 
himself  can  say.  We  have  not  alluded  to  one  or  two  remon- 
strances on  questions  of  absolute  fact,  which  are  beside  the  pre- 
sent purpose. 

Both  kinds  of  encyclopaedic  works  have  been  fashioned  upon 
predecessors,  from  the  very  earliest  which  had  a  predecessor  to  be 
founded  upon ;  and  the  undertakings  before  us  will  be  themselves 
the  ancestors  of  a  line  of  successors.  Those  who  write  in  such 
collections  should  be  careful  what  they  say,  for  no  one  can  tell 
how  long  a  misstatement  may  live.  On  this  point  we  will  give 
the  history  of  a  pair  of  epithets.  When  the  historian  De  Thou 
died,  and  left  the  splendid  library  which  was  catalogued  by 
Bouillaud  and  the  brothers  Dupuis  (Bullialdus  and  Puteanus), 
there  was  a  manuscript  of  De  Thou's  friend  Vieta,  the  Harmonicon 
Cceleste,  of  which  it  is  on  record,  under  Bouillaud's  hand,  that  he 
himself  lent  it  to  Cosmo  de'  Medici,  to  which  must  be  added  that 
M.  Libri  found  it  in  the  Magliabecchi  Library  at  Florence  in  our 
own  day.  Bouillaud,  it  seems,  entirely  forgot  what  he  had  done. 
Something,  probably,  that  Peter  Dupuis  said  to  Bouillaud,  while 
they  were  at  work  on  the  catalogue,  remained  on  his  memory, 
and  was  published  by  him  in  1 645,  long  after ;  to  the  effect  that 
Dupuis  lent  the  manuscript  to  Mersenne,  from  whom  it  was  pro- 
cured by  some  intending  plagiarist,  who  would  not  give  it  back. 
This  was  repeated  by  Sherburne,  in  1675,  who  speaks  of  the  work, 
which  '  being  communicated  to  Mersennus  was,  by  some  perfidious 
acquaintance  of  that  honest-minded  person,  surreptitiously  taken 
from  him,  and  irrecoverably  lost  or  suppressed,  to  the  unspeakable 
detriment  of  the  lettered  world.'  Now  let  the  reader  look  through 
the  dictionaries  of  the  last  century  and  the  present,  scientific  or 
general,  at  the  article  '  Vieta,'  and  he  will  be  amused  with  the 
constant  recurrence  of  '  honest-minded  '  Mersenne,  and  his  '  surrep- 
titious' acquaintance.  We  cannot  have  seen  less  than  thirty 
copies  of  these  epithets. 

October  18,  1862.  Correspondence  of  Scientific  Men  of  the  Seven- 
teenth Century,  in  the  Collection  of  the  Earl  of  Macclesfield.  2 
vols.  (Oxford,  University  Press.) 

Though  the  title-page  of  this  collection  bears  date  1841,  it  is 
only  just  completed  by  the  publication  of  its  Table  of  Contents 
and  Index.  Without  these,  a  work  of  the  kind  is  useless  for 


REVIEW  OF  MACCLESFIELD  LETTERS.          449 

consultation,  and  cannot  make  its  way.  The  reason  of  the  delay 
will  appear:  its  effect  is  well  known  to  us.  We  have  found 
inquirers  into  the  history  of  science  singularly  ignorant  of  things 
which  this  collection  might  have  taught  them. 

In  the  same  year,  1841,  the  Historical  Society  of  Science, 
which  had  but  a  brief  existence,  published  a  collection  of  letters, 
eighty-three  in  number,  edited  by  Mr.  Halliwell,  of  English  men 
of  science,  which  dovetails  with  the  one  before  us,  and  is  for  the 
most  part  of  a  prior  date.  The  two  should  be  bound  up  together. 
The  smaller  collection  runs  from  1562  to  1682  ;  the  larger,  from 
1606  to  past  1700.  We  shall  speak  of  the  two  as  the  Museum 
collection  and  the  Macclesfield  collection.  And  near  them 
should  be  placed,  in  every  scientific  library,  the  valuable  collec- 
tion published,  by  Mr.  Edleston,  for  Trinity  College,  in  1850. 

The  history  of  these  letters  runs  back  to  famous  John  Collins, 
the  attorney-general  of  the  mathematics,  as  he  has  been  called, 
who  wrote  to  everybody,  heard  from  everybody,  and  sent  copies  of 
everybody's  letter  to  everybody  else.  He  was  in  England  what 
Mersenne  was  in  France  :  as  early  as  1671,  E.  Bernard  addresses 
him  as  '  the  very  Mersennus  and  intelligence  of  this  age.'  John 
Collins  was  never  more  than  accountant  to  the  Excise  Office,  to 
which  he  was  promoted  from  teaching  writing  and  ciphering,  at 
the  Kestoration  :  he  died  in  1682.  We  have  had  a  man  of  the 
same  office  in  our  own  day,  the  late  Prof.  Schumacher,  who  made 
the  little  Danish  Observatory  of  Altona  the  junction  of  all  the 
lines  by  which  astronomical  information  was  conveyed  from  one 
country  to  another.  When  the  collision  took  place  between 
Denmark  and  the  Duchies,  the  English  Government,  moved  by 
the  Astronomical  Society,  instructed  its  diplomatic  agents  to 
represent  strongly  to  the  Danish  Government,  when  occasion 
should  arise,  the  great  importance  of  the  Observatory  of  Altona 
to  the  astronomical  communications  of  the  whole  world.  But 
Schumacher  had  his  own  celebrated  journal,  the  Astronomische 
Nachrichten,  by  which  to  work  out  part  of  his  plan ;  private 
correspondence  was  his  supplementary  assistant.  Collins  had 
only  correspondence  to  rely  on.  Nothing  is  better  known  than 
that  it  was  Collins's  collection  which  furnished  the  materials  put 
forward  by  the  Committee  of  the  Eoyal  Society  in  1712,  us  a 
defence  of  Newton  against  the  partisans  of  Leibnitz.  The  noted 
Commercium  Epistolicum  is  but  the  abbreviation  of  a  title 
which  runs  on  with  '  D.  Johannis  Collins  et  aliorum  .  .  .' 

The  whole  of  this  collection  passed  into  the  hands  of  William 
Jones,  the  father  of  the  Indian  Judge  of  the  same  name,  who 

G  G 


450  A  BUDGET  OF  PAEADOXES. 

died  in  1749.  Jones  was  originally  a  teacher,  but  was  presented 
with  a  valuable  sinecure  by  the  interest  of  George,  second  Earl  of 
Macclesfield,  the  mover  of  the  bill  for  the  change  of  style  in 
Britain,  who  died  President  of  the  Eoyal  Society.  This  change  of 
style  may  perhaps  be  traced  to  the  union  of  energies  which  were 
brought  into  concert  by  the  accident  of  a  common  teacher :  Lord 
Macclesfield  and  Lord  Chesterfield,  the  mover  and  seconder,  and 
Daval,  who  drew  the  bill,  were  pupils  of  De  Moivre.  Jones,  who 
was  a  respectable  mathematician  though  not  an  inventor,  collected 
the  largest  mathematical  library  of  his  day,  and  became  possessor 
of  the  papers  of  Collins,  which  contained  those  of  Oughtred  and 
others.  Some  of  these  papers  passed  into  the  custody  of  the 
Eoyal  Society  :  but  the  bulk  was  either  bequeathed  to,  or  pur- 
chased by,  Lord  Macclesfield ;  and  thus  they  found  their  way  to 
Shirburn  Castle,  where  they  still  remain. 

A  little  before  1836,  this  collection  attracted  the  attention  of  a 
searching  inquirer  into  points  of  mathematical  history,  the  late 
Prof.  Eigaud,  who  died  in  1839.  He  examined  the  whole 
collection  of  letters,  obtained  Lord  Macclesfield's  consent  to  their 
publication,  and  induced  the  Oxford  Press  to  bear  the  expense. 
It  must  be  particularly  remembered  that  there  still  remains  at 
Shirburn  Castle  a  valuable  mass  of  non-epistolary  manuscripts. 
So  far  as  we  can  see,  the  best  chance  of  a  further  examination  and 
publication  lies  in  public  encouragement  of  the  collection  now 
before  us:  the  Oxford  Press  might  be  induced  to  extend  its 
operations  if  it  were  found  that  the  results  were  really  of  interest 
to  the  literary  and  scientific  world.  Eigaud  died  before  the  work 
was  completed,  and  the  publication  was  actually  made  by  one  of 
his  sons,  S.  Jordan  Eigaud,  who  died  Bishop  of  Antigua.  But 
this  publication  was  little  noticed,  for  the  reasons  given.  The 
completion  now  published  consists  of  a  sufficient  table  of  contents, 
of  the  briefest  kind,  by  Prof.  De  Morgan,  and  an  excellent 
index  by  the  Eev.  John  Eigaud.  The  work  is  now  fairly  started 
on  its  career. 

If  we  were  charged  to  write  a  volume  with  the  title  '  Small 
things  in  their  connexion  with  great,'  we  could  not  do  better 
than  choose  the  small  part  of  this  collection  of  letters  as  our 
basis.  The  names,  as  well  as  the  contents,  are  both  great  and 
small :  the  great  names,  those  which  are  known  to  every  mathe- 
matician who  has  any  infusion  of  the  history  of  his  pursuit,  are 
Briggs,  Oughtred,  Charles  Cavendish,  Grascoigne,  Seth  Ward, 
Wallis,  Hu[y]gens,  Collins,  William  Petty,  Hooke,  Boyle,  Pell, 
Oldenburg,  Brancker,  Slusius,  Bertit,  Bernard,  Borelli,  Mouton, 


REVIEW   OF  MACCLESFIELD   LETTERS.  451 

Pardies,  Fermat,  Towneley,  Auzout,  D.  Gregory,  Halley,  Machin, 
Montmort,  Cotes,  Jones,  Saunderson,  Reyneau,  Brook  Taylor, 
Maupertuis,  Bouguer,  La  Condamine,  Folkes,  Macclesfield,  Baker, 
Barrow,  Flamsteed,  Lord  Brounker,  J.  Gregory,  Newton  and 
Keill.  To  these  the  Museum  collection  adds  the  names  of 
Thomas  Digges,  Dee,  Tycho  Brahe,  Harriot,  Lydyat,  Briggs, 
Warner,  Tarporley,  Pell,  Lilly,  Oldenburg,  Collins,  Morland. 

The  first  who  appears  on  the  scene  is  the  celebrated  Oughtred, 
who  is  related  to  have  died  of  joy  at  the  Restoration  :  but  it 
should  be  added,  by  way  of  excuse,  that  he  was  eighty-six  years 
old.  He  is  an  animal  of  extinct  race,  an  Eton  mathematician. 
Few  Eton  men,  even  of  the  minority  which  knows  what  a  sliding 
rule  is,  are  aware  that  the  inventor  was  of  their  own  school  and 
college :  but  they  may  be  excused,  for  Dr.  Hutton,  so  far  as  his 
Dictionary  bears  witness,  seems  not  to  have  known  it  any  more 
than  they.  A  glance  at  one  of  his  letters  reminds  us  of  a  letter 
from  the  Astronomer  Royal  on  the  discovery  of  Neptune,  which 
we  printed  March  20,  1847.  Mr.  Airy  there  contends,  and  proves 
it  both  by  Leverrier  and  by  Adams,  that  the  limited  publication 
of  a  private  letter  is  more  efficient  than  the  more  general  pub- 
lication of  a  printed  memoir.  The  same  may  be  true  of  a  dead 
letter,  as  opposed  to  a  dead  book.  Our  eye  was  caught  by  a 
letter  of  Oughtred  (1629),  containing  systematic  use  of  con- 
tractions for  the  words  sine,  cosine,  &c.,  prefixed  to  the  symbol  of 
the  angle.  This  is  so  very  important  a  step,  simple  as  it  is,  that 
Euler  is  justly  held  to  have  greatly  advanced  trigonometry  by  its 
introduction.  Nobody  that  we  know  of  has  noticed  that  Oughtred 
was  master  of  the  improvement,  and  willing  to  have  taught  it,  if 
people  would  have  learnt.  After  looking  at  his  dead  letter,  we 
naturally  turned  to  his  dead  book  on  trigonometry,  and  there  we 
found  the  abbreviations  s,  sco,  £,  too,  se,  seco,  regularly  established 
as  part  of  the  system  of  the  work.  But  not  one  of  those  who 
have  investigated  the  contending  claims  of  Euler  and  Thomas 
Simpson  has  chanced  to  know  of  Oughtred's  '  Trigonometric ' : 
and  the  present  revival  is  due  to  his  letter,  not  to  his  book. 

A  casual  reader,  turning  over  the  pages,  would  imagine  that 
almost  all  the  letters  had  been  printed,  either  in  the  General 
Dictionary,  or  in  Birch,  &c. :  so  often  does  the  supplementary 

remark  begin  with  '  this  letter  has  been  printed  in .'  For 

ourselves  we  thought,  until  we  counted,  that  a  large  majority  of 
the  letters  had  been  given,  either  in  whole  or  in  part.  But  the 
positive  strikes  the  mind  more  forcibly  than  the  negative :  we 
find  that  all  of  which  any  portion  has  been  in  type  makes  up  very 

001 


452  A  BUDGET  OF  PARADOXES. 

little  more  than  a  quarter  ;  the  cases  in  which  the  whole  letter  is 
given  being  a  minority  of  this  quarter.  The  person  who  has 
been  best  ransacked  is  Flamsteed  :  of  36  letters  from  him,  34  had 
been  previously  given  in  whole  or  in  part.  Of  59  letters  to  and 
from  Newton,  only  17  have  been  culled. 

The  letters  have  been  modernized  in  spelling,  and,  to  some 
extent,  in  algebraical  notation ;  it  also  seems  that  conjectural 
methods  of  introducing  interpolations  into  the  text  have  been 
necessary.  For  all  this  we  are  sorry  :  the  scientific  value  of  the 
'collection  is  little  altered,  but  its  literary  value  is  somewhat 
•lowered.  But  it  could  not  be  helped:  the  printers  could  not 
work  from  the  originals,  and  Prof.  Eigaud  had  to  copy  every- 
thing himself.  A  fac-simile  must  have  been  the  work  of  more 
time  than  he  had  to  give  :  had  he  attempted  it,  his  death  would 
have  cut  short  the  whole  undertaking,  instead  of  allowing  him  to 
prepare  everything  but  a  preface,  and  to  superintend  the  printing 
of  one  of  the  volumes.  We  may  also  add,  that  we  believe  we 
have  notices  of  all  the  letters  in  the  Macclesfield  collection.  We 
judge  this  because  several  which  are  too  trivial  to  print  are  num- 
bered and  described ;  and  those  would  certainly  not  have  been 
noticed  if  any  omissions  had  been  made.  And  we  know  that 
every  letter  was  removed  from  Shirburn  Castle  to  Oxford. 

Two  persons  emerge  from  oblivion  in  this  series  of  letters. 
The  first  is  Michael  Dary,  an  obscure  mathematician,  who  was  in 
correspondence  with  Newton  and  other  stars.  He  was  a  gauger 
at  Bristol,  by  the  interest  of  Collins  ;  afterwards  a  candidate  for 
the  mathematical  school  at  Christ's  Hospital,  with  a  certificate 
from  Newton :  he  was  then  a  gunner  in  the  Tower,  and  is  lastly 
described  by  Wallis  as  '  Mr.  Dary,  the  tobacco-cutter,  a  knowing 
man  in  algebra.'  In  1674,  Dary  writes  to  Newton  at  Cambridge, 
as  follows  : — '  Although  I  sent  you  three  papers  yesterday,  I 
cannot  refrain  from  sending  you  this.  I  have  had  fresh  thoughts 
.this  morning.'  Two  months  afterwards  poor  Newton  writes  to 
Collins,  '  Mr.  Dary  is  very  solicitous  about  mathematics ' :  but,  in 
spite  of  the  persecution,  he  subscribes  himself  to  Dary  'your 
loving  friend.'  Dary's  problem  is  that  of  finding  the  rate  of 
interest  of  an  annuity  of  which  the  value  and  term  are  given. 
Dary's  theorem,  which  he  seems  to  have  invented  specially  for 
the  solution  of  his  problem,  though  it  is  of  wide  range,  can  be 
exhibited  to  mathematical  readers  even  in  our  columns.  In 
modern  language,  it  is  that  the  limit  of  <j>nx,  when  n  increases 
without  limit,  is  a  solution  of  (£>x  =  x.  We  have  mentioned  the 
I.  Newton  to  whom  Dary  looked  up ;  we  add  a  word  about  the 


REVIEW   OF   MACCLESFIELD  LETTEES.  453 

one  on  whom  be  looked  down.  Dr.  John  Newton,  a  sedulous 
publisher  of  logarithms,  tables  of  interest,  &c.,  who  began  his 
career  before  Isaac  Newton,  sometimes  puzzles  those  who  do  not 
know  him,  when  described  as  I.  Newton.  The  scientific  world 
was  of  opinion  that  all  that  was  valuable  in  one  of  his  works  was 
taken  from  Dary's  private  communications. 

The  second  character  above  alluded  to  is  one  who  carried 
mathematical  researches  a  far  greater  length  than  Newton  him- 
self: the  assistance  which  he  rendered  in  this  respect,  even  to 
Newton,  has  never  been  acknowledged  in  modern  times :  though 
the  work  before  us  shows  that  his  contemporaries  were  fully  aware 
of  it,  and  never  thought  of  concealing  it.  In  his  theory  of 
gravitation,  in  which,  so  far  as  he  went,  we  have  every  reason  to 
believe  he  was  prior  to  Newton,  he  did  not  extend  his  calculations 
to  the  distance  of  the  moon ;  his  views  in  this  matter  were  purely 
terrestrial,  and  led  him  to  charge  according  to  weight.  He  was 
John  Stiles,  the  London  and  Cambridge  carrier :  his  name  is  a 
household  word  in  the  Macclesfield  Letters,  and  is  even  enshrined 
in  the  depths  of  Birch's  quartos.  Dary  informs  Newton — let  us 
do  his  memory  this  justice — that  he  had  paid  John  Stiles  for 
the  carriage.  At  the  time  when  the  railroad  to  Cambridge  was 
opened,  a  correspondent  recommended  the  directors,  in  our 
columns,  to  call  an  engine  by  the  name  of  John  Stiles,  and  never 
to  let  that  name  go  off  the  road.  We  do  not  know  whether  the 
advice  was  followed :  if  not,  we  repeat  it. 

Little  points  of  life  and  manners  come  out  occasionally. 
Baker,  the  author  of  a  work  on  algebra  much  esteemed  at  the 
time,  wrote  to  Collins  that  their  circumstances  are  alike,  '  having 
a  just  equal  number  of  chargeable  olive-branches,  and  being  in 
the  same  predicament  and  blessed  condemnation  with  you,  not 
more  preaching  than  unpaid,  and  preaching  the  art  of  content- 
ment to  others,  am  forced  to  practise  it.'  But  the  last  sentence 
of  his  letter  runs  as  follows  : — '  I  have  sent  by  the  bearer  .  .  , 
twenty  shillings,  as  a  token  to  you  ;  desiring  you  to  accept  of  it, 
as  a  small  taste  from  Yours,  Thos.  Baker.'  In  our  day,  men  of 
a  station  to  pay  parish  taxes  do  not  offer  their  friends  hard  money 
to  buy  liquor.  But  Flamsteed  writes  to  Collins  as  follows  : — 
i  Last  week  he  sent  us  down  the  counterpart,  which  my  father 
has  sealed,  and  I  return  up  to  you  by  the  carrier,  with  51.  to  be 
paid  to  Mr.  Leneve  for  the  writing.  I  have  added  2s.  Gd.  over, 
which  will  pay  the  expenses  and  serve  to  drink,  with  him.'  This 
would  seem  as  odd  to  us  as  it  would  have  seemed  thirty  years  ago 
that  half-a-crown  should  pay.  carriage  for  a  deed  from  Derby  to 


454  A  BUDGET  OF  PARADOXES. 

London,  and  leave  margin  for  a  bottle  of  wine :  in  our  day,  the 
Post-office  and  the  French  treaty  would  just  manage  it  between 
them.  But  Flamsteed  does  not  limit  his  friend  to  one  -bottle  ;  he 
adds,  '  If  you  expend  more  than  the  half-crown,  I  will  make  it 
good  after  Whitsuntide.'  Collins  does  not  remember  exactly 
where  he  had  met  James  Gregory,  and  mentions  two  equally  likely 
places  thus  : — *  Sir,  it  was  once  my  good  hap  to  meet  with  you  in 
an  alehouse,  or  in  Sion  College.'  There  is  a  little  proof  how 
universally  the  dinner-hour  was  twelve  o'clock.  Astronomers  well 
know  the  method  of  finding  time  by  equal  altitudes  of  the  sun 
before  and  after  noon  :  Huyghens  calls  it  '  le  moyen  de  deux 
egales  hauteurs  du  soleil  devant  et  apres  diner.' 

There  is  one  mention  of  *  Mr.  Cocker,  our  famous  English 
graver  and  writer,  now  a  schoolmaster  at  Northampton.'  This 
is  the  true  Cocker :  his  genuine  works  are  specimens  of  writing, 
such  as  engraved  copy-books,  including  some  on  arithmetic,  with 
copper-plate  questions  and  space  for  the  working  ;  also  a  book  of 
forms  for  law-stationers,  with  specimens  of  legal  handwriting.  It 
is  recorded  somewhere  that  Cocker  and  another,  whose  name  we 
forget,  competed  with  the  Italians  in  the  beauty  of  their  flourishes. 
This  was  his  real  fame  :  and  in  these  matters  he  was  great.  The 
eighth  edition  of  his  book  of  law  forms  (1675),  published  shortly 
after  Cocker's  death,  has  a  preface  signed  '  J.  H.'  This  was  John 
Hawkins,  who  became  possessed  of  Cocker's  papers — at  least  he 
said  so — and  subsequently  forged  the  famous  Arithmetic,  a 
second  work  on  Decimal  Arithmetic,  and  an  English  dictionary, 
all  attributed  to  Cocker.  The  proofs  of  this  are  set  out  in 
De  Morgan's  '  Arithmetical  Books.'  Among  many  other  corro- 
borative circumstances,  the  clumsy  forger,  after  declaring  that 
Cocker  to  his  dying  day  resisted  strong  solicitation  to  publish  his 
Arithmetic,  makes  him  write  in  the  preface  an  Ille  ego  qui 
quondam  of  this  kind  : — '  I  have  been  instrumental  to  the  benefit 
of  many,  by  virtue  of  those  useful  arts,  writing  and  engraving ; 
and  do  now,  with  the  same  wonted  alacrity,  cast  this  my 
arithmetical  mite  into  the  public  treasury.'  The  book  itself  is 
not  comparable  in  merit  to  at  least  half-a-dozen  others.  How 
then  comes  Cocker  to  be  the  impersonation  of  Arithmetic  ? 
Unless  some  one  can  show  proof,  which  we  have  never  found,  that 
he  was  so  before  1756,  the  matter  is  to  be  accounted  for  thus. 

Arthur  Murphy,  the  dramatist,  was  by  taste  a  man  of  letters, 
and  ended  by  being  the  translator  of  Tacitus ;  though  many  do 
not  know  that  the  two  are  one.  His  friends  had  tried  to  make 
a  man  of  business ;  and  no  doubt  he  had  been  well  plied 


REVIEW   OF   MACCLESFIELD   LETTERS.  455 

with  commercial  arithmetic.  His  first  dramatic  performance,  the 
farce  of  'The  Apprentice,'  produced  in  1756,  is  about  an  idle 
young  man  who  must  needs  turn  actor.  Two  of  the  best  known 
books  of  the  day  in  arithmetic  were  those  of  Cocker  and  Wingate. 
Murphy  chooses  Wingate  to  be  the  name  of  an  old  merchant 
who  delights  in  vulgar  fractions,  and  Cocker  to  be  his  arithmetical 
catchword — '  You  read  Shakspeare  !  get  Cocker's  Arithmetic ! 
you  may  buy  it  for  a  shilling  on  any  stall ;  best  book  that  ever 
was  wrote  ! ' :  and  so  on.  The  farce  became  very  popular,  and,  as 
we  believe,  was  the  means  of  elevating  Cocker  to  his  present 
pedestal,  where  Wingate  would  have  been,  if  his  name  had  had 
the  droller  sound  of  the  two  to  English  ears. 

A  notoriety  of  an  older  day  turns  up,  Major-General  Lambert. 
The  common  story  is  that  he  was  banished  to  Guernsey,  where  he 
passed  thirty  years  in  confinement,  rearing  and  painting  flowers. 
But  Baker,  in  1678,  represents  him  as  a  prisoner  at  Plymouth, 
sending  equations  for  solution  as  a  challenge :  probably  his  place 
of  confinement  was  varied,  and  his  occupation  also. 

[General  Lambert  was  removed  to  Plymouth,  probably  about 
1668.  His  daughter  captured  the  son  of  the  Governor  of 
Guernsey,  who  therefore  probably  was  reckoned  an  unsafe 
custodier  thenceforward ;  though  he  assured  the  king  that  he  had 
turned  the  young  couple  out  of  doors,  and  had  never  given  them 
a  penny.  Great  importance  was  attached  to  Lambert's  safe 
detention  :  probably  the  remaining  republicans  looked  upon  him 
as  to  be  their  next  Cromwell,  if  such  a  thing  were  to  be.  There 
were  standing  orders  to  shoot  him  at  once  on  the  first  appearance 
of  any  enemy  before  the  island.  See  Notes  and  Queries,  3rd  S. 
iv.  89.] 

Collins  informs  James  Gregory  that  'some  of  the  Royal 
Academy  wrote  over  to  Mr.  Oldenburg,  who  was  desired  to 
impart  the  same  to  the  Council  of  the  Royal  Society,  that  the 
French  King  was  willing  to  allow  pensions  to  one  or  two  learned 
Englishmen,  but  they  never  made  any  answer  to  such  a  proposal.' 
This  was  written  in  1671.,  and  the  thing  probably  happened  several 
years  before.  Mr.  De  Morgan  communicated  the  account  of  the 
proposal  to  Lord  Macaulay,  who  replied  that  he  did  not  think  that 
any  Englishman  received  a  literary  pension  from  Louis ;  but  that 
there  is  a  curious  letter,  about  1664,  from  the  French  Ambassador, 
in  which  he  says  that  he  has,  by  his  master's  orders,  been  making 
inquiries  as  to  the  state  of  learning  in  England,  and  that  he  is 
sorry  to  find  that  the  best  writer  is  the  infamous  M'dtonus.  On 
two  such  independent  testimonies  it  may  be  held  proved  that  tks 


456  A   BUDGET   OF  PARADOXES. 

French  King  had  attempted  to  buy  a  little  adherence  from 
English  literature  and  science  ;  and  the  silent  contempt  of  the 
Eoyal  Society  is  an  honourable  fact  in  their  history. 

Another  little  bit  of  politics  is  as  follows.  Oughtred  is 
informed  that  'Mr.  Foster,  our  Lecturer  on  Astronomy  at 
Gfresham  College,  is  put  out  because  he  will  not  kneel  down  at 
the  communion-table.  A  Scotsman  [Mungo  Murray],  one  that  is 
verbi  bis  minister,  is  now  lecturer  in  Mr.  Foster's  place.'  Ward, 
in  his  work  on  the  Grresham  Professors,  suppresses  the  reason,  and 
the  suppression  lowers  the  character  of  his  book.  Foster  was 
expelled  in  1636,  and  re-elected  on  a  vacancy  in  1641,  when 
Puritanism  had  gained  strength. 

The  correspondence  of  Newton  would  require  deeper  sifting 
than  could  be  given  in  such  an  article  as  the  present.  The  first 
of  the  letters  (1669)  is  curious,  as  presenting  the  appearance  of 
forms  belonging  to  the  great  calculus  which,  in  this  paragraph, 
we  ought  to  call  that  of  fluxions.  We  find,  of  the  date  February 
18,  1669—70,  what  we  believe  is  the  earliest  manifestation  of  that 
morbid  part  of  Newton's  temperament  which  has  been  so  variously 
represented.  He  had  solved  a  problem — being  that  which  we 
have  called  Dary's — on  which  he  writes  as  follows  :  '  The  solution 
of  the  annuity  problem,  if  it  will  be  of  any  use,  you  have  my 
leave  to  insert  it  into  the  Philosophical  Transactions,  so  it  be 
without  my  name  to  it.  For  I  see  not  what  there  is  desirable  in 
.public  esteem,  were  I  able  to  acquire  and  maintain  it.  It  would 
perhaps  increase  my  acquaintance,  the  thing  which  I  chiefly 
study  to  decline.' 

Three  letters  touch  upon  '  the  experiment  of  glass  rubbed  to 
cause  various  motions  in  bits  of  paper  underneath ' :  they  are 
supplements  to  the  account  given  by  Newton  to  the  Royal 
Society,  and  printed  by  Birch.  It  was  Newton,  so  far  as  appears, 
who  added  glass  to  the  substances  known  to  be  electric.  Soon 
afterwards  we  come  to  a  little  bit  of  the  history  of  the  appoint- 
ment to  the  Mint.  It  has  appeared  from  the  researches  of  late 
years  that  Newton  was  long  an  aspirant  for  public  employment : 
the  only  coolness  which  is  known  to  have  taken  place  between 
him  and  Charles  Montague  [Halifax]  arose  out  of  his  imagining 
that  his  friend  was  not  in  earnest  about  getting  him  into  the 
public  service.  March  14,  1696,  Newton  writes  thus  to  Halley : 
— *  And  if  the  rumour  of  preferment  for  me  in  the  Mint  should 
hereafter,  upon  the  death  of  Mr.  Hoar  [the  comptroller],  or  any 
other  occasion,  be  revived,  I  pray  that  you  would  endeavour  to 
.obviate  it  by  acquainting  your  friends  that  I  neither  put  in  for 


REVIEW    OF   MACCLESFIELD   LETTERS.  457 

any  place  in  the  Mint,  nor  would  meddle  with  Mr.  Hoar's 
place,  were  it  offered  to  me.'  This  means  that  Mr.  Hoar's  place 
had  been  suggested,  which  Newton  seems  to  have  declined.  Five 
days  afterwards,  Montague  writes  to  Newton  that  he  is  to  have  the 
Wardenship.  It  is  fair  to  Newton  to  say  that  in  all  probability 
this  was  not — or  only  in  a  smaller  degree — a  question  of  personal 
dignity,  or  of  salary.  It  must  by  this  time  have  been  clear  to 
him  that  the  minister,  though  long  bound  to  make  him  an  object 
of  patronage,  was  actually  seeking  him  for  the  Mint,  because 
he  wanted  both  Newton's  name  and  his  talents  for  business — 
which  he  knew  to  be  great — in  the  weighty  and  dangerous  opera- 
tion of  restoring  the  coinage.  It  may  have  been,  and  probably 
was,  the  case  that  Newton  had  a  tolerably  accurate  notion  of 
what  he  would  have  to  do,  and  of  what  degree  of  power  would  be 
necessary  to  enable  him  to  do  it  in  his  own  way. 

We  have  said  that  the  non-epistolary  manuscripts  are  still 
unexamined.  There  is  a  chance  that  one  of  them  may  answer  a 
question  of  two  centuries'  standing,  which  is  worth  answering, 
because  it  has  been  so  often  asked.  About  1640,  Warner,  after- 
wards assisted  by  Pell,  commenced  a  table  of  antilogarithms,  of 
the  kind  which  Dodson  afterwards  constructed  anew  and  pub- 
lished. In  the  Museum  collection  there  is  inquiry  after  inquiry 
from  Charles  Cavendish,  first,  as  to  when  the  Analogies,  as  he 
called  them,  would  be  finished ;  next,  when  they  would  be 
printed.  Pell  answers,  in  1644,  that  Warner  left  his  papers  to  a 
kinsman,  who  had  become  bankrupt,  and  proceeds  thus  : — 

'  I  am  not  a  little  afraid  that  all  Mr.  Warner's  papers,  and  no  small 
share  of  my  labours  therein,  are  seazed  upon,  and  most  unmathemati- 
cally  divided  between  the  sequestrators  and  creditors,  who  (not  being 
able  to  ballance  the  account  where  there  appeare  so  many  numbers, 
and  much  troubled  at  the  sight  of  so  many  crosses  and  circles  in  the 
superstitious  Algebra  and  that  black  art  of  Geometry)  will,  no  doubt, 
determine  once  in  their  lives  to  become  figure-casters,  and  so  vote 
them  all  to  be  throwen  into  the  fire,  if  some  good  body  doe  not  reprieve 
them  for  pye-bottoms,  for  which  purposes  you  know  analogicall 
numbers  are  incomparably  apt,  if  they  be  accurately  calculated.' 

Pell  afterwards  told  Wallis  that  the  papers  had  fallen  into  the 
hands  of  Dr.  Busby,  and  Collins  writes  that  they  were  left  in  the 
hands  of  Dr.  Thorndike,  a  prebendary  of  Westminster ;  whence 
Eigaud  seems  to  say  that  Thorndike  had  left  them  to  Dr.  Busby. 
Birch  says  that  he  procured  for  the  Eoyal  Society  four  boxes  from 
Busby's  trustees,  containing  papers  of  Warner  and  Pell:  but 
there  is  no  other  tradition  of  such  things  in  the  Society.  But  in 


458  A   BUDGET   OF   PARADOXES. 

the  Birch  manuscripts  at  the  British  Museum,  there  turns  up, 
as  printed  in  what  we  call  the  Museum  collection,  a  list  of 
Warner's  papers,  with  Collinses  receipt  to  Dr.  Thorndike  at  the 
bottom,  and  engagement  to  restore  them  on  demand.  The  date 
is  December  14,  1667  ;  Wallis's  statement  being  in  1693.  It  is 
possible  that  Busby  may  be  a  mistake  altogether  :  he  was  very 
unlikely  to  have  had  charge  of  any  mathematical  papers :  there 
may  have  been  a  confusion  between  the  Prebendary  of  West- 
minster and  the  Head  Master  of  Westminster  School.  If  so,  in 
all  probability  Thorndike  handed  the  cumbrous  lot  over  to  the 
notorious  collector  of  mathematical  papers,  blessing  himself  that 
he  had  got  rid  of  them  in  a  manner  which  would  insure  their 
return  if  he  were  called  upon  by  the  owners  to  restore  them.  It 
is  much  against  this  hypothesis  that  Dodson,  who  certainly  re- 
calculated, can  say  nothing  more  about  Warner  than  a  repetition 
of  Wallis's  story :  though,  had  Collins  kept  the  papers,  they 
would  probably  have  been  in  Jones's  possession  at  the  very  time 
when  Dodson,  who  was  a  friend  of  Jones  and  a  user  of  his 
library,  was  engaged  on  his  own  computations.  But  even  books, 
and  still  more  manuscripts,  are  often  singularly  overlooked  ;  and 
it  remains  not  very  improbable  that  Warner's  table  is  now  at 
Shirburn  Castle,  among  the  unexamined  manuscripts. 


Redit  labor  actus  in  orbem.  Among  the  matters  which  have 
come  to  me  since  the  Budget  opened,  there  is  a  pamphlet  of 
quadrature  of  two  pages  and  a  half  from  Prof.  Recalcati,  already 
mentioned.  It  ends  with  "Quelque  objection  qu'on  fasse  touch- 
ant  les  raisonnements  ci-dessus  on  tombera  toujours  dans  1'ab- 
surde.'  A  civil  engineer — so  he  says — has  made  the  quadrature 
"  no  longer  a  problem,  but  an  axiom."  As  follows :  "  Take  the 
quadrant  of  a  circle  whose  circumference  is  given,  square  the 
quadrant  which  gives  the  true  square  of  the  circle.  Because 
30-4-4  =  7*5  x  7*5  =  56-25  =  the  positive  square  of  a  circle  whose 
circumference  is  30."  Brevity,  the  soul  of  wit,  is  the  "  wings  of 
mighty  winds  "  to  quadrature,  and  sends  it  "  flying  all  abroad." 
A  surbodhicary — something  like  M.A.  or  LL.D.,  I  understand — 
at  Calcutta,  published  in  1863  the  division  of  an  angle  into  any 
odd  number  of  parts,  demonstration  and  all  in  —  when  the 
diagram  is  omitted — one  page,  good-sized,  well-leaded  type,  small 
duodecimo.  But  in  the  Preface  he  acknowledges  "sheer  in- 
ability "  to  execute  his  task.  Mr.  William  Dean,  of  Todmorden, 
in  1863,  announced  3^  as  proved  both  practically  and  geome- 


CYCLOMETKY  AND  STEEL  PENS.  459 

trically :  he  has  been  already  mentioned  anonymously.  Next 
I  have  the  tract  of  Don  Juan  Larriva,  published  at  Leiria  in 
1856,  and  dedicated  to  Queen  Victoria.  Mr.  W.  Peters,  already 
mentioned,  who  has  for  some  months  been  circulating  diagrams 
on  a  card,  publishes  (August,  1865)  'The  Circle  Squared.'  He 
agrees  with  the  Archpriest  of  St.  Vitus.  He  hints  that  a  larger 
publication  will  depend  partly  on  the  support  he  receives,  and 
partly  on  the  castigation,  for  which  last,  of  course,  he  looks  to 
me.  Cyclometers  have  their  several  styles  of  wit ;  so  have  anti- 
cyclometers  too,  for  that  matter.  Mr.  Peters  will  not  allow  me 
any  extra-journal  being :  I  am  essentially  a  quotation  from  the 
Athenceum ;  '  A.  De  Morgan '  et  prceterea  nihil.  If  he  had  to 
pay  for  keeping  me  set  up,  he  would  find  out  his  mistake,  and 
would  be  glad  to  compound  handsomely  for  a  stereotype.  Next 
comes  a  magnificent  sheet  of  pasteboard,  printed  on  .both  sides. 
Having  glanced  at  it  and  detected  quadrature,  I  began  methodi- 
cally at  the  beginning — '  By  Eoyal  Command,'  with  the  lion 
and  unicorn,  and  all  that  comes  between.  Mercy  on  us !  thought 
I  to  myself:  has  Her  Majesty  referred  the  question  to  the 
Judicial  Committee  of  the  Privy  Council,  where  all  the  great 
difficulties  go  now-a-days,  and  is  this  proclamation  the  result? 
On  reading  further  I  was  relieved  by  finding  that  the  first  side 
is  entirely  an  advertisement  of  Joseph  Gillott's  steel  pens,  with 
engraving  of  his  premises,  and  notice  of  novel  application  of  his 
unrivalled  machinery.  The  second  side  begins  with  '  the  circle 
rectified  '  by  W.  E.  Walker,  who  finds  TT=  3-141 5947896241 55  .  .  . 
This  is  an  off-shoot  from  an  accurate  geometrical  rectification, 
on  which  it  is  to  be  presumed  Mr.  Gillott's  new  machinery 
is  founded.  I  have  no  doubt  that  Mr.  Walker's  error,  which  is 
only  in  the  sixth  place  of  decimals,  will  not  hurt  the  pens,  unless 
it  be  by  the  slightest  possible  increase  of  the  tendency  to  open  at 
the  points.  This  arises  from  Mr.  Walker  having  rectified  above 
proof  by -000002136034362  .  .  . 

Lastly,  I,  even  I  myself,  who  have  long  felt  that  I  was  a 
quadrature  below  par,  have  solved  the  problem  by  means  which, 
in  the  present  state  of  the  law  of  libel,  I  dare  not  divulge.  But 
the  result  is  permitted ;  and  it  goes  far  to  explain  all  the  dis- 
cordances. The  ratio  of  the  circumference  to  the  diameter  is  not 
always  the  same  !  Not  that  it  varies  with  the  radius  ;  the  geo- 
meters are  right  enough  on  that  point :  but  it  varies  with  the 
time,  in  a  manner  depending  upon  the  difference  of  the  true 
longitudes  of  the  Sun  and  Moon.  A  friend  of  mine — at  least 
until  he  misbehaved — insisted  on  the  mean  right  ascensions  :  but 


4CO  A   BUDGET   OF  PARADOXES. 

I  served  him  as  Abraham  served  his  guest  in  Franklin's  parable. 
The  true  formula  is,  A  and  a  being  the  Sun's  and  Moon's  longi- 
tudes, 

IT  =3^  +  ^008  (A -a). 

Mr.  James  Smith  obtained  his  quadrature  at  full  moon  ;  the 
Archpriest  of  St.  Vitus  and  some  others  at  new  moon.  Until  I 
can  venture  to  publish  the  demonstration,  I  recommend  the 
reader  to  do  as  I  do,  which  is  to  adopt  3-14159  .  .  .  .  ,  and  to 
think  of  the  matter  only  at  the  two  points  of  the  lunar  month  at 
which  it  is  correct.  The  Nautical  Almanac  will  no  doubt  give 
these  points  in  a  short  time :  I  am  in  correspondence  with  the 
Admiralty,  with  nothing  to  get  over  except  what  I  must  call: 
a  perverse  notion  on  the  part  of  the  Superintendent  of  the 
Almanac,  who  suspects  one  correction  depending  on  the  Moon's 
latitude ;  and  the  Astronomer  Eoyal  leans  towards  another  de- 
pending on  the  date  of  the  Queen's  accession.  I  have  no 
patience  with  these  men  :  what  can  the  Moon's  node  or  the 
Queen's  reign  possibly  have  to  do  with  the  ratio  in  question  ? 
But  this  is  the  way  with  all  the  regular  men  of  science ;  Newton 
is  to  them  &c.  &c.  &c.  &c. 

The  following  method  of  finding  the  circumference  of  a  circle 
(taken  from  a  paper  by  Mr.  S.  Drach  in  the  Phil.  Mag.,  Jan. 
1863,  Suppl.)  is  as  accurate  as  the  use  of  3-14159265.  From 
three  diameters  deduct  8-thousandths  and  7-millionths  of  a 
diameter;  to  the  result  add  five  per  cent.  We  have  then  not 
quite  enough  ;  but  the  shortcoming  is  at  the  rate  of  about  an 
inch  and  a  sixtieth  of  an  inch  in  14,000  miles. 


Though  I  have  met  with  nothing  but  a  little  tract  from  the 
school  of  Jacob  Behmen  (or  Bohme ;  I  keep  to  the  old  English 
version  of  his  name),  yet  there  has  been  more,  and  of  a  more 
recent  date.  I  am  told  of  an  '  Introduction  to  Theosophy  \_Theo 
privative,  I  suppose,  as  in  theological]  ;  or,  the  Science  of  the 
Mystery  of  Christ,'  published  in  1854,  mostly  from  the  writings 
of  William  Law  :  and  also  of  a  volume  of  688  pages,  of  the  same 
year,  printed  for  private  circulation,  containing  notes  for  a 
biography  of  William  Law.  The  editor  of  the  first  work  wishes 
to  grow  '  a  generation  of  perfect  Christians '  by  founding  a 
Theosophic  College,  for  which  he  requests  the  public  to  raise  a 
hundred  thousand  pounds.  There  is  a  good  account  of  Jacob 
Behmen  in  the  Penny  Cyclopcedia.  The  author  mentions  in- 
accurate accounts,  one  of  which  he  quotes,  as  follows :  '  He 


JACOB   BEHMEN.  401 

derived   all   his   mystical   and  rapturous  doctrine  from  Wood's 

*  Athense  Oxonienses,'  vol.  i.  p.  610,  and  '  Hist,  et  Antiq.  Acad. 
Oxon.,'  vol.  ii.  p.  308.'     On  which  the  author  remarks  that  Wood 
was   born    after   Behmen's  death.      There   must    have    been    a 
few  words  which   slipped  out :  what  is  meant   is  that  Behmen 

•  derived  his  doctrine  from  Robert  Fludd,  for  whom  see  Wood's 
&c.  &c.'     Even  this  is  absurd   enough :  for    Behmen  began   to 
publish  in  1610,  and  Fludd  in  1616.     Fludd  was  a  Eosicrucian, 
and  a  mystic  of  a  different  type  from  Behmen.     I  have  some  of 
his  works,  and   could   produce  out  of  them  paradoxes  enough, 
according  to  our  ways  of  thinking,  to  fit  out  a  host.     But  the 
Rosicrucian  system  was  a  recognised  school  of  its  day,  and  Fludd, 
a  man   of  great  learning,  had  abettors    enough  in  all  which  he 
advanced,  and  predecessors  in  most  of  it. 

[A  Correspondent  has  recently  sent  a  short  summary  of  the  claims 
of  Jacob  Behmen  to  rank  higher  than  I  have  placed  him.  I  shall 
gladly  insert  this  summary  in  the  book  I  contemplate,  as  a  state- 
ment of  what  is  said  of  Behmen  far  less  liable  to  suspicion  of  ex- 
aggeration than  anything  I  could  write.  I  shall  add  a  few  extracts 
from  Behmen  himself,  in  support  of  his  right  to  be  in  my  list.] 

*  Jacob  Behmen. — That  Prof.  De  Morgan  classes  Jacob  Behmen 
among  paradoxers  can  only  be  attributed  to  the  fact  of  his  being 
avowedly  unacquainted  with  the  writings  of  that  author.  Per- 
haps you  may  think  a  few  words  from  one  who  knows  them  well 
of  sufficient  interest  to  the  learned  Professor,  and  your  readers  in 
general,  to  be  worthy  of  space  in  your  columns.  The  meta- 
physical system  of  Behmen — the  most  perfect  and  only  true  one 
— still  awaits  a  qualified  commentator.  Behmen's  countryman, 
Dionysius  Andreas  Freher,  who  spent  the  greater  part  of  his  life 
in  this  country,  and  whose  exposition  of  Behmen  exists  only  in 
MS.,  filling  many  volumes,  written  in  English,  with  the  excep- 
tion of  two,  written  in  German,  with  numerous  beautiful,  highly 
ingenious,  and  elaborate  illustrations, — copies  of  some  of  which 
are  in  the  British  Museum,  but  all  the  originals  of  which  are  in 
the  possession  of  the  'gentleman  who  is  the  editor  of  the  two 
works  alluded  to  by  Prof.  De  Morgan, — this  .Freher  was  the  first 
to  philosophically  expound  Behmen's  system,  which  was  after- 
wards, with  the  help  of  these  MSS.,  as  it  were,  popularized  by 
William  Law  ;  but  both  Freher  and  Law  confined  themselves 
chiefly  to  its  theological  aspect.  In  Behmen,  however,  is  to  be 
found,  not  only  the  true  ground  of  all  theology,  but  nl^o  that 
of  all  physical  science.  He  demonstrated  with  a  fullness,  accu- 


462  A  BUDGET   OF  PARADOXES. 

racy,  completeness  and  certainty  that  leave  nothing  to  be  desired, 
the  innermost  ground  of  Deity  and  Nature ;  and,  confining 
myself  to  the  latter,  I  can  from  my  own  knowledge  assert,  that  in 
Behmen's  writings  is  to  be  found  the  true  and  clear  demonstra- 
tion of  every  physical  fact  that  has  been  discovered  since  his  day. 
Thus,  the  science  of  electricity,  which  was  not  yet  in  existence 
when  he  wrote,  is  there  anticipated ;  and  not  only  does  Behmen 
describe  all  the  now  known  phenomena  of  that  force,  but  he  even 
gives  us  the  origin,  generation  and  birth  of  electricity  itself. 
Again,  positive  evidence  can  be  adduced  that  Newton  derived  all 
his  knowledge  of  gravitation  and  its  laws  from  Behmen,  with 
whom  gravitation  or  attraction  is,  and  very  properly  so,  as  he 
shows  us,  the  first  of  the  seven  properties  of  Nature.  The  theory 
defended  by  Mr.  Grove,  at  the  Nottingham  meeting  of  last  year, 
that  all  the  apparently  distinct  causes  of  moral  and  physical 
phenomena  are  but  so  many  manifestations  of  one  central  force, 
and  that  Continuity  is  the  law  of  nature,  is  clearly  laid  down,  and 
its  truth  demonstrated,  by  Behmen,  as  well  as  the  distinction 
between  spirit  and  matter,  and  that  the  moral  and  material 
world  is  pervaded  by  a  sublime  unity.  And  though  all  this  was 
not  admitted  in  Behmen's  days,  because  science  was  not  then 
sufficiently  advanced  to  understand  the  deep  sense  of  our  author, 
many  of  his  passages,  then  unintelligible,  or  apparently  absurd, 
read  by  the  light  of  the  present  age,  are  found  to  contain  the 
positive  enunciation  of  principles  at  whose  discovery  and  estab- 
lishment science  has  only  just  arrived  by  wearisome  and  painful 
investigations.  Every  new  scientific  discovery  goes  to  prove  his 
profound  and  intuitive  insight  into  the  most  secret  workings  of 
nature;  and  if  scientific  men,  instead  of  sharing  the  prejudice 
arising  from  ignorance  of  Behmen's  system,  would  place  them- 
selves on  the  vantage  ground  it  affords,  they  would  at  once  find 
themselves  on  an  eminence  whence  they  could  behold  all  the 
arcana  of  nature.  Behmen's  system,  in  fact,  shows  us  the  inside 
of  things,  while  modern  physical  science  is  content  with  looking 
at  the  outside.  Behmen  traces  back  every  outward  manifesta- 
tion or  development  to  its  one  central  root, — to  that  one  central 
energy  which,  as  yet,  is  only  suspected  ;  every  link  in  the  chain 
of  his  demonstration  is  perfect,  and  there  is  not  one  link  wanting. 
He  carries  us  from  the  outbirths  of  the  circumference,  along  the 
radius  to  the  centre,  or  point,  and  beyond  that  even  to  the  zero, 
demonstrating  the  constitution  of  the  zero,  or  nothing,  with 
mathematical  precision.  C.  W.  H.' 

And  so  Behmen  is  no  subject  for  the  Budget  I     I  waited  until  I 


JACOB   BEHMEN.  463 

should  chance  to  light  on  one  of  his  volumes,  knowing  that  any 
volume  would  do,  and  almost  any  page.  My  first  hap  was  on  the 
second  volume  of  the  edition  of  1664  (4to,  published  by  M. 
Eichardson)  and  opening  near  the  beginning,  a  turn  or  two 
brought  me  to  page  13,  where  I  saw  about  sulphur  and  mercurius 
as  follows : — 

Thus  SUL  is  the  soul,  in  an  herb  it  is  the  oil,  and  in  man  also,  ac- 
cording to  the  spirit  of  this  world  in  the  third  principle,  which  is  con- 
tinually generated  out  of  the  anguish  of  the  will  in  the  mind,  and  the 
Brimstone- worm  is  the  Spirit,  which  hath  the  fire  and  burneth  :  PHUR 
is  the  sour  wheel  in  itself  which  causeth  that. 

Mercurius  comprehcndeth  all  the  four  forms,  even  as  the  life  springeth 
up.  and  yet  hath  not  its  dark  beginning  in  the  Center  as  the  PHUR 
hath,  but  after  the  flash  of  fire,  when  the  sour  dark  form  is  terrified, 
where  the  hardness  is  turned  into  pliant  sharpness,  and  where  the 
second  will  (viz.  the  will  of  nature,  which  is  called  the  Anguish) 
ariseth,  there  .Mercurius  hath  its  original.  For  MER  is  the  shivering 
wheel,  very  horrible,  sharp,  venomous,  and  hostile  ;  which  assimulateth 
it  thus  in  the  sourness  in  the  flash  of  fire,  where  the  sour  wrathful  life 
ariseth.  The  syllable  CU  is  the  pressing  out,  of  the  Anxious  will  of 
the  mind,  from  Nature :  which  is  climbing  up,  and  wllleth  to  be  out 
aloft.  RI  is  the  comprehension  of  the  flash  of  fire,  which  in  MER 
giveth  a  clear  sound  and  tune.  For  the  flash  maketh  the  tune,  and  it 
is  the  Salt-Spirit  which  soundeth,  and  its  form  (or  quality)  is  gritty 
like  sand,  and  herein  arise  noises,  sounds,  and  voices,  and  thus  CU 
comprehendeth  the  flash,  and  so  the  pressure  is  as  a  wind,  which 
thrusteth,  and  giveth  a  spirit  to  the  flash,  so  that  it  liveth  and  burneth. 
Thus  the  syllable  US  is  called  the  burning  fire,  which  with  the  spirit 
continually  driveth  itself  forth  :  and  the  syllable  CU  presseth  con- 
tinually upon  the  flash. 

Shades  of  Tauler  and  Paracelsus,  how  strangely  you  do  mix  ! 
Well  may  Hallam  call  Germany  the  native  soil  of  Mysticism. 
Had  Behmen  been  the  least  of  a  scholar,  he  would  not  have 
divided  sulph-ur  and  merc-ur-i-us  as  he  has  done  : — and  the 
inflexion  us,  that  boy  of  all  work,  would  have  been  rejected.  I 
think  it  will  be  held  that  a  writer  from  whom  hundreds  of  pages 
like  the  above  could  be  brought  together,  is  fit  for  the  Budget. 
If  Sampson  Arnold  Mackay  had  tied  his  etymologies  to  a  mystical 
Christology,  instead  of  a  mystical  infidelity,  he  might  have  had 
a  school  of  followers.  The  nonsense  about  Newton  borrowing 

O 

gravitation  from  Behmen  passes  only  with  those  who  know  neither 
what  Newton  did,  nor  what  was  done  before  him. 

The  above  reminds  me  of  a  class  of  paradoxers  whom  I  wonder 
that  I  forgot ;  they  are  without  exception  the  greatest  bores  of 


464  A   BUDGET   OF  PARADOXES. 

all,  because  they  can  put  the  small  end  of  their  paradox  into  any 
literary  conversation  whatsoever,  I  mean  the  people  who  have 
heard  the  local  pronunciation  of  celebrated  names,  and  attempt 
not  only  to  imitate  it,  but  to  impose  on  others  their  broken 
Crerman  or  Arabic,  or  what  not.  They  also  learn  the  vernacular 
names  of  those  who  are  generally  spoken  of  in  their  Latin  forms  ; 
at  least,  they  learn  a  few  cases,  and  hawk  them  as  evidences  of 
erudition.  They  are  miserably  mistaken  :  scholarship,  as  a  rule, 
always  accepts  the  vernacular  form  of  a  name  which  has  vernacular 
celebrity.  Hallam  writes  Behmen :  his  index-maker,  rather 
superfluously,  gives  'Behmen  or  Boehm.'  And  he  retains 
Melanchthon,  the  name  given  by  Keuchlin  to  his  little  kinsman 
Schwartzerd,  because  the  world  has  adopted  it :  but  he  will 
none  of  Capnio,  the  name  which  Reuchlin  fitted  on  to  himself, 
because  the  world  has  not  adopted  it.  He  calls  the"  old  forms 
pedantry :  but  he  sees  that  the  rejection  of  well-established 
results  of  pedantry  would  be  greater  pedantry  still.  The  para- 
doxers  assume  the  question  that  it  is  more  correct  to  sound  a  man 
by  lame  imitation  of  his  own  countrymen  than  as  usual  in  the 
country  in  which  the  sound  is  to  be  made.  Against  them  are, 
first,  the  world  at  large  ;  next,  an  overpowering  majority  of  those 
who  know  something  about  surnames  and  their  history.  Some 
thirty  years  ago — a  fact — there  appeared  at  the  police-office  a 
complainant  who  found  his  own  law.  In  the  course  of  his  argu- 
ment, he  asked,  '  What  does  Kitty  say  ?  ' — '  Who's  Kitty  ? '  said 
the  magistrate,  '  your  wife,  or  your  nurse  ? ' — '  Sir  !  I  mean  Kitty, 
the  celebrated  lawyer.' — '  Oh  ! '  said  the  magistrate,  '  I  suspect 
you  mean  Mr.  Chitty,  the  author  of  the  great  work  on  pleading.' 
— '  I  do  sir  !  but  Chitty  is  an  Italian  name,  and  ought  to  be  pro- 
nounced Kitty'  This  man  was  a  full-blown  flower :  but  there  is 
many  a  modest  bud  ;  and  all  ought  either  to  blush  when  seen  or 
to  waste  their  pronunciation  on  the  desert  air. 

I  stand  up  for  king  Custom,  or  Usus,  as  Horace  called  him, 
with  whom  is  arbitrium  the  decision,  and  jus  the  right,  and  norma 
the  way  of  deciding,  simply  because  he  has  potestas  the  power- 
He  may  admit  one  and  another  principle  to  advise  :  but  Custom 
is  not  a  constitutional  king ;  he  may  listen  to  his  cabinet,  but  he 
decides  for  himself:  and  if  the  ministry  should  resign,  he  blesses 
his  stars  and  does  without  them.  We  have  a  glorious  liberty  in 
England  of  owning  neither  dictionary,  grammar,  nor  spelling- 
book  :  as  many  as  choose  write  by  either  of  the  three,  and  decide 
all  disputed  points  their  own  way,  those  following  them  who  please. 

Throughout  this  book  I  have  called  people  by  the  names  which 


KING   CUSTOM'S   ADVISERS.  465 

denote  them  in  their  books,  or  by  our  vernacular  names.  This  is 
the  intelligible  way  of  proceeding.  I  might,  for  instance  (p.  31), 
have  spoken  of  Charles  de  Bovelles,  of  Lefevre  d'Etaples,  of  Pelerin, 
and  of  Etienne.  J^ut  I  prefer  the  old  plan.  Those  who  like 
another  plan  better,  are  welcome  to  substitute  with  a  pen,  when 
they  know  what  to  write ;  when  they  do  not,  it  is  clear  that  they 
would  not  have  understood  me  if  I  had  given  modern  names. 

The  principal  advisers  of  King  Custom  are  as  follows.  First, 
there  is  Etymology,  the  chiffonnier,  or  general  rag-merchant,  who 
has  made  such  a  fortune  of  late  years  in  his  own  business  that  he 
begins  to  be  considered  highly  respectable.  He  gives  advice 
which  is  more  thought  of  than  followed,  partly  on  account  of  the 
fearful  extremes  into  which  he  runs.  He  lately  asked  some  boys 
of  sixteen,  at  a  matriculation  examination  in  English,  to  what 
branch  of  the  Indo-Grermanic  family  they  felt  inclined  to  refer 
the  Pushto  language,  and  what  changes  in  the  force  of  the  letters 
took  place  in  passing  from  Grreek  into  Moeso-Grothic.  Because 
all  syllables  were  once  words,  he  is  a  little  inclined  to  insist  that 
they  shall  be  so  still.  He  would  gladly  rule  English  with  a 
Saxon  rod,  which  might  be  permitted  with  a  certain  discretion 
which  he  has  never  attained  :  and  when  opposed,  he  defends  him- 
self with  the  analogies  of  the  Aryan  family  until  those  who  hear 
him  long  for  the  discovery  of  an  Athanasyus.  He  will  transport 
a  word  beyond  seas — he  is  recorder  of  Ehematopolis — on  circum- 
stantial evidence  which  looks  like  mystery  gone  mad  ;  but,  strange 
to  say,  something  very  often  comes  to  light  after  sentence  passed 
which  proves  the  soundness  of  the  conviction. 

The  next  adviser  is  Logic,  a  swearing  old  justice  of  peace, 
quorum,  and  rotulorum,  whose  excesses  brought  on  such  a  fit  of 
the  gout  that  for  many  years  he  was  unable  to  move.  He  is  now 
mending,  and  his  friends  say  he  has  sown  his  wild  oats.  He  has 
some  influence  with  the  educated  subjects  of  Custom,  and  will 
have  more,  if  he  can  learn  the  line  at  which  interference  ought  to 
stop :  with  them  he  has  succeeded  in  making  an  affirmative  of 
two  negatives ;  but  the  vulgar  won't  never  have  nothing  to  say 
to  him.  He  has  always  railed  at  Milton  for  writing  that  Eve 
was  the  fairest  of  her  daughters  ;  but  has  never  satisfactorily  shown 
what  Milton  ought  to  have  said  instead. 

The  third  adviser  has  more  influence  with  the  mass  of  the 
subjects  of  King  Custom  than  the  other  two  put  together;  his 
name  is  Fiddlefaddle,  the  toy-shop  keeper  ;  and  the  other  two 
put  him  forward  to  do  their  worst  work.  In  return,  he  often  uses 
their  names  without  authority.  He  took  Etymology  to  witness 

H  H 


466  A  BUDGET   OF  PARADOXES. 

that  means  to  an  end  must  be  plural :  and  he  would  have  any  one 
method  to  be  a  mean.    But  Etymology  proved  him  wrong,  King 
Custom  referred  him  to   his  Catechism,  in  which   is  'a  means 
whereby  we  receive  the  same,'  and   Analogy — a  subordinate   of 
Etymology — asked  whether  he  thought   it  a  great  new  to  hear 
that  he  was  wrong.     It  was  either  this  Fiddle-faddle,  or  Lindley 
Murray  his  traveller,  who  persuaded  the  Miss  Slipslops,  of  the 
Ladies   Seminary,  to   put  '  The  Misses  Slipslop '  over  the  gate: 
Sixty  years  ago,  this  bagman  called  at  all  the  girls'  schools,  and 
got  many  of  the  teachers  to  insist  on  the  pupils  saying  '  Is  it  not' 
and  '  Can  I  not '  for  '  Isn't  it '  and  '  Can't  I ' :  of  which  it  came 
that  the  poor  girls  were  dreadfully  laughed  at  by  their  irreverent 
brothers  when  they  went  home  for  the  holidays.     Had  this  bad 
adviser  not  been  severely  checked,  he  might  by  this  time  have 
proposed  our  saying '  The  Queen's  of  England  son,'  declaring,  in  the 
name  of  Logic,  that  the  prince  was  the  Queen's  son,  not  England's. 
Lastly,   there    is    Typography   the  metallurgist,  an   executive 
officer  who  is  always  at  work  in  secret,  and  whose  lawless  mode  of 
advising  is  often  done  by  carrying  his  notions  into  effect  without 
leave   given.       He  it  is  who  never  ceases  suggesting  that  the 
same  word  is  not  to  occur  in  a  second  place  within  sight  of  the 
first.     When  the  Authorized  Version  was  first  printed,  he  began 
this  trick  at  the   passage,  'Let  there  be    light,  and  there  was 
light ; '  he  drew  a  line  on  the  proof  under  the  second  light,  and 
wrote  '  luminosity  ? '  opposite.     He  is  strongest  in  the  punctua- 
tions  and  other    signs ;    he  has    a  pepper-box    full  of    commas 
always  by  his  side.     He   puts  everything  under  marks  of  quota- 
tion which  he  has  ever  heard  before.     An  earnest  preacher,  in  a 
very  moving  sermon,  used  the  phrase  Alas  !  and  alack  a  day ! 
Typography  stuck  up  the  inverted  commas  because  he  had  read 
the  old  Anglo-Indian  toast,  '  A  lass  and  a  lac  a  day ! '     If  any 
one  should  have  the  sense  to  leave   out  of  his    Greek  the   un- 
meaning scratches  which  they  call  accents,  he  goes  to  a  lexicon 
and  puts  them  in.     He  is  powerful  in  routine  ;  but  when  two 
routines  interlace  or  overlap,  he  frequently  takes  the  wrong  one. 

Subject  to  bad  advice,  and  sometimes  misled  for  a  season,  King 
Custom  goes  on  his  quiet  way,  and  is  sure  to  be  right  at  last. 
Treason  does  never  prosper  :  what's  the  reason  ? 
Why,  when  it  prospers,  none  dare  call  it  treason. 

Language  is  in  constant  fermentation,  and  all  that  is  thrown  in, 
so  far  as  it  is  not  fit  to  assimilate,  is  thrown  off;  and  this 
without  any  obvious  struggle.  In  the  meanwhile  every  one  who 
has  read  good  authors,  from  Shakspeare  downward,  knows  what 


TEST   OF  LANGUAGE.  467 

is  and  what  is  not  English  ;  and  knows,  also,  that  our  language 

O  '  '  y  O  O 

is  not  one  and  indivisible.  Two  very  different  turns  of  phrase 
may  both  be  equally  good,  and  as  good  as  can  be  :  we  may  be 
relieved  of  the  consequences  of  contempt  of  one  court  by  habeas 
corpus  issuing  out  of  another. 

Hallam  remarks  that  the  Authorized  Version  of  the  Bible  is 
not  in  the  language  of  the  time  of  James  the  First :  that  it  is 
not  the  English  of  Kaleigh  or  of  Bacon.  Here  arises  the  ques- 
tion whether  Kaleigh  and  Bacon  are  the  true  expositors  of  the 
language  of  their  time ;  and  whether  they  were  not  rather  the 
incipient  promoters  of  a  change  which  was  successfully  resisted 
by — among  other  things — the  Authorized  Version  of  the  Testa- 
ments. I  am  not  prepared  to  concede  that  I  should  have  given 
to  the  English  which  would  have  been  fashioned  upon  that  of 
Bacon  by  imitators,  such  as  they  usually  are,  the  admiration 
which  is  forced  from  me  by  Bacon's  English  from  Bacon's  pen. 
On  this  point  we  have  a  notable  pai'allel.  Samuel  Johnson 
commands  our  admiration,  at  least  in  his  matured  style  :  but  we 
nauseate  his  followers.  It  is  an  opinion  of  mine  that  the  works 
of  the  leading  writers  of  an  age  are  seldom  the  proper  specimens 
of  the  language  of  their  day,  when  that  language  is  in  its  state  of 
progression.  I  judge  of  a  language  by  the  colloquial  idiom  of 
educated  men :  that  is,  I  take  this  to  be  the  best  medium 
between  the  extreme  cases  of  one  who  is  ignorant  of  grammar 
and  one  who  is  perched  upon  a  style.  Dialogue  is  what  I  want 
to  judge  by,  and  plain  dialogue :  so  I  choose  Robert  Eecorde 
and  his  pupil  in  the  '  Castle  of  Knowledge,'  written  before  1556. 
When  Dr.  Eobert  gets  into  his  altitudes  of  instruction,  he  differs 
from  his  own  common  phraseology  as  much  as  probably  did 
Bacon  when  he  wrote  morals  and  philosophy.  But  every  now 
and  then  I  come  to  a  little  plain  talk  about  a  common  thing,  of 
which  I  propose  to  show  a  specimen.  Anything  can  be  made  to  look 
old  by  such  changes  as  makes  into  maketh,  with  a  little  old  spelling. 
I  shall  invert  these  changes,  using  the  newer  form  of  inflexion, 
and  the  modern  spelling ':  with  no  other  variation  whatever. 

'  Scholar.  Yet  the  reason  of  that  is  easy  enough  to  be  con- 
ceived, for  when  the  day  is  at  the  longest  the  Sun  must  needs 
shine  the  more  time,  and  so  must  it  needs  shine  the  less  time 
when  the  day  is  at  the  shortest :  this  reason  I  have  heard  many 
men  declare. 

Master.  That  may  be  called  a  crabbed  reason,  for  it  goes 
backward  like  a  crab.  The  day  makes  not  the  Sun  to  shine,  but 
the  Sun  shining  makes  the  day.  And  so  the  length  of  the  day 

H    It    '1 


468  A  BUDGET   OF  PARADOXES. 

makes  not  the  Sun  to  shine  long,  neither  the  shortness  of  the 
day  causes  not  [sic]  the  Sun  to  shine  the  lesser  time,  but  con- 
trariwise the  long  shining  of  the  Sun  makes  the  long  day,  and 
the  short  shining  of  the  Sun  makes  the  lesser  day :  else  answer 
me  what  makes  the  days  long  or  short? 

Scholar.     I  have  heard  wise  men  say  that  Summer  makes  the 
long  days,  and  Winter  makes  the  long  nights. 

Master.     They  might  have  said  more  wisely,  that  long  days 
makes  summer  and  short  days  make  winter. 

Scholar.     Why,  all  that  seems  one  thing  to  me. 
Master.     Is  it  all  one  to  say,  God  made  the  earth,  and  the 
earth   made    God?     Covetousness   overcomes    all  men,    and   all 
men  overcome  covetousness  ? 

Scholar.  No,  not  so ;  for  here  the  effect  is  turned  to  be  the 
cause,  and  the  agent  is  made  the  patient. 

Master.  So  is  it  to  say  Summer  makes  long  days,  when  you 
should  say :  Long  days  make  summer. 

Scholar.  I  perceive  it  now  :  but  I  was  so  blinded  with  the 
vulgar  error,  that  if  you  had  demanded  of  me  further  what  did 
make  the  summer,  I  had  been  like  to  have  answered  that  green 
leaves  do  make  summer ;  and  the  sooner  by  remembrance  of  an 
old  saying  that  a  year  should  come  in  which  the  summer  should 
not  be  known  but  by  the  green  leaves. 

Master.  Yet  this  saying  does  not  import  that  green  leaves  do 
make  summer,  but  that  they  betoken  summer ;  so  are  they  the 
sign  and  not  the  cause  of  summer.' 

I  have  taken  a  whole  -page  of  our  author,  without  omission, 
that  the  reader  may  see  that  I  do  not  pick  out  sentences   con- 
venient for  my  purpose.      I  have  done  nothing  but  alter  the 
third  person    of  the  verb  and   the   spelling:    but  great   is  the 
effect    thereof.      We    say   '  the    Sun    shining   makes  the  day : ' 
Recorde,  '  the  Sonne  shynynge  maketh  the  daye.'     These  points 
apart,  we  see  a  resemblance  between  our  English  and  that  of  three 
hundred  years  ago,  in  the  common  talk  of  educated  persons,  which 
will  allow  us  to  affirm  that  the  language  of  the  authorized  Bible 
must  have  been  very  close  to  that  of  its  time.     For   I  cannot 
admit  that  much  change  can  have  taken  place  in  fifty  years  :  and 
the  language  of  the  version  represents  both  our  common  English 
and    that   of    Recorde   with    very   close    approximation.      Take 
sentences  from  Bacon  and  Raleigh,  and  it  will  be  apparent  that 
the.«e  writers  will  be  held  to  differ  from  all  three,  Recorde,  the 
version,  and  ourselves,  by  differences  of  the  same  character.     But 
we  speak  of  Recorde's  conversation,  and  of  our  own.     We   con- 
clude that  it  is  the  plain  and  almost  colloquial  character  of  the 


PRONUNCIATION.  469 

Authorized  Version  which  distinguishes  it  from  the  English  of 
Bacon  and  Ealeigh,  by  approximating  it  to  the  common  idiom  of 
the  time.  If  any  one  will  cast  an  eye  upon  the  letters  of  instruc- 
tion written  by  Cecil  and  the  Bishop  of  London  to  the  translators 
themselves,  or  to  the  general  directions  sent  to  them  in  the  King's 
name,  he  will  find  that  these  plain  business  compositions  differ 
from  the  English  of  Bacon  and  Raleigh  by  the  same  sort  of 
differences  which  distinguish  the  version  itself. 

The  foreign  word,  or  the  word  of  a  district,  or  class  of  people, 
passes  into  the  general  vernacular;  but  it  is  long  before  the 
specially  learned  will  acknowledge  the  right  of  those  with  whom 
they  come  in  contact  to  follow  general  usage.  The  rule  is 
simple :  so  long  as  a  word  is  technical  or  local,  those  who  know 
its  technical  or  local  pronunciation  may  reasonably  employ  it. 
But  when  the  word  has  become  general,  the  specialist  is  not  very 
wise  if  he  refuse  to  follow  the  mass,  and  perfectly  foolish  if  he 
insist  on  others  following  him.  There  have  been  a  few  who 
demanded  that  Euler  should  be  pronounced  in  the  German 
fashion  :  Euler  has  long  been  the  property  of  the  world  at  large  ; 
what  does  it  matter  how  his  own  countrymen  pronounce  the 
letters  ?  Shall  we  insist  on  the  French  pronouncing  Newton 
without  that  final  tong  which  they  never  fail  to  give  him  ? 
They  would  be  wise  enough  to  laugh  at  us  if  we  did.  We  re- 
member that  a  pedant  who  was  insisting  on  all  the  pronuncia- 
tions being  retained,  was  met  by  a  maxim  in  contradiction, 
invented  at  the  moment,  and  fathered  upon  Kaen-foo-tzee,  an 
authority  which  he  was  challenged  to  dispute.  Whom  did  you 
speak  of  ?  said  the  bewildered  man  of  accuracy.  Learn  your  own 
system,  was  the  answer,  before  you  impose  it  on  others ;  Confu- 
cius says  that  too. 

The  old  English  has  fote,  fode,  loke,  coke,  roke,  &c.,  for  foot, 
&c.  And  above  rhymes  in  Chaucer  to  remove.  Suspecting  that 
the  broader  sounds  are  the  older,  we  may  surmise  that  remove  and 
food  have  retained  their  old  sounds,  and  that  cook,  once  coke, 
would  have  rhymed  to  our  Luke,  the  vowel  being  brought  a  little 
nearer,  perhaps,  to  the  o  in  our  present  coke,  the  fuel,  probably  so 
called  as  used  by  cooks.  If  this  be  so,  the  Chief  Justice  Cook,  of 
our  lawyers,  and  the  Coke  (pronounced  like  the  fuel)  of  the 
greater  part  of  the  world,  are  equally  wrong.  The  lawyer  has  no 
right  whatever  to  fasten  his  pronunciation  upon  us :  even  leaving 
aside  the  general  custom,  he  cannot  prove  himself  right,  and  is 
probably  wrong.  Those  who  know  the  village  of  Rokeby  (pro- 
nounced Rookby)  despise  the  world  for  not  knowing  how  to  name 
Walter  Scott's  poem :  that  same  world  never  asked  a  question 


470  A   BUDGET   OF   PAKADOXES. 

about  the  matter,  and  the  reception  of  the  parody  of  Jokeby, 
which  soon  appeared,  was  a  sufficient  indication  of  their  notion. 
Those  who  would  fasten  the  hodiernal  sound  upon  us  may  be 
reminded  that  the  question  is,  not  what  they  call  it  now,  but 
what  it  was  called  in  Cromwell's  time.  Throw  away  general 
usage  as  a  lawgiver,  and  this  is  the  point  which  emerges. 
Probably  Ruke-by  would  be  right,  with  a  little  turning  of  the 
Italian  u  towards  6  of  modern  English. 

[Some  of  the  above  is  from  an  old  review.  I  do  not  always 
notice  such  insertions  :  I  take  nothing  but  my  own  writings.  A 
friend  once  said  to  me, '  Ah  !  you  got  that  out  of  the  Athenaeum,  \ ' 
*  Excuse  me,'  said  I,  l  the  Athenceum  got  that  out  of  me  ! '] 

It  is  part  of  my  function  to  do  justice  to  any  cyclometers 
whose  methods  have  been  wrongly  described  by  any  orthodox 
sneerers  (myself  included).  In  this  character  I  must  notice 
Dethlevus  Cluverius,  as  the  Leipzig  Acts  call  him  (probably 
Dethleu  Cluvier),  grandson  of  the  celebrated  geographer,  Philip 
Cluvier.  The  grandson  was  a  Fellow  of  the  Koyal  Society, 
elected -on  the  same  day  as  Halley,  November  30,  1678:  I 
suppose  he  lived  in  England.  This  man  is  quizzed  in  the  Leipzig 
Acts  for  1686;  and,  if  Montucla  insinuate  rightly,  by  Leibnitz, 
who  is  further  suspected  of  wanting  to  embroil  Cluvier  with  his 
own  opponent  Nieuwentiit,  on  the  matter  of  infinitesimals.  So 
far  good  :  I  have  nothing  against  Leibnitz,  who  though  he  was 
ironical,  told  us  what  he  laughed  at.  But  Montucla  has  behaved 
very  unfairly :  he  represents  Cluvier  as  placing  the  essence  of  his 
method  in  the  solution  of  the  problem  construere  mundum 
divince  menti  analogum,  to  construct  a  world  corresponding  to 
the  divine  mind.  Nothing  to  begin  with  :  no  way  of  proceeding. 
Now,  it  ought  to  have  been  ex  dqta  lined  construere,  &c. :  there 
is  a  given  line,  which  is  something  to  go  on.  Further,  there  is  a 
way  of  proceeding:  it  is  to  find  the  product  of  1,  2,  3,  4,  &c.  for 
ever.  Moreover,  Montucla  charges  Cluvier  with  unsquaring  the 
parabola,  which  Archimedes  had  squared  as  tight  as  a  glove. 
But  he  never  mentions  how  very  nearly  Cluvier  agrees  with  the 
Greek  :  they  only  differ  by  1  divided  by  3n2,  where  n  is  the  infinite 
number  of  parts  of  which  a  parabola  is  composed.  This  must 
have  been  the  conceit  that  tickled  Leibnitz,  and  made  him  wish 
that  Cluvier" and  Nieuwentiit  should  fight  it  out.  Cluvier,  was 

O  x 

adm'tted,  on  terms  of  irony,  into  the  Leipzig  Acts :  he  appeared 
on  a  more  serious  footing  in  London.  It  is  very  rare  for 
one  cyclometer  to  refute  another :  les  corsaires  ne  se  battent  pas 
The  only  instance  I  recall  is  that  of  M.  Cluvier,  who  (Phil. 


THE   RAINBOW   PARADOX.  471 

Trans.  1686,  No.  185)  refuted  M.  Mallemont  de  Messange,  who 
published  at  Paris  in  1686.  He  does  it  in  a  very  serious  style, 
and  shows  himself  a  mathematician.  And  yet  in  the  year  in 
which,  in  the  Phil.  Trans.-,  he  was  a  geometer,  and  one  who 
rebukes  his  squarer  for  quoting  Matthew  xi.  25,  in  that  very  year 
he  was  the  visionary  who,  in  the  Leipzig  Acts,  professed  to  build 
a  world  resembling  the  divine  mind  by  multiplying  together 
1,  2,  3,  4,  &c.  up  to  infinity. 

There  is  a  very  pretty  opening  for  a  paradox  which  has  never 
found  its  paradoxer  in   print.     The  philosophers  teach   that  the 
rainbow  is   not  material :    it  comes  from  rain-drops,   but  those 
rain-drops  do  not  take  colour.      They  only  give  it,  as  lenses  and 
mirrors  ;  and   each   one   drop   gives  all  the  colours,  but  throws 
them  in  different  directions.      Accordingly,  the  same  drop  which 
furnishes  red  light  to  one  spectator  will  furnish  violet  to  another, 
properly  placed.      Enter  the  paradoxer  whom  I  have  to  invent. 
The  philosopher  has  gulled  you  nicely.     Look  into  the  water,  and 
you   will  see  the  reflected  rainbow :    take   a  looking-glass  held 
sideways,  and  you  see  another  reflexion.     How  could  this  be,  if 
there  were  nothing  coloured  to  reflect  ?      The  paradoxer's  facts 
are  true :  and  what  are  called  the  reflected  rainbows  are  other 
rainbows,  caused  by  those  other  drops  which  are   placed  so  as  to 
give  the  colours  to  the  eye  after  reflexion,  at  the  water  or  the 
looking-glass.     A  few  years  ago  an  artist  exhibited  a  picture  with 
a  rainbow  and  its  apparent  reflexion  :  he  simply  copied  what  he 
had  seen.     When  his  picture  was  examined,  some  started  the  idea 
that  there  could  be  no  reflexion  of  a  rainbow  ;  they  were  right : 
they  inferred  that  the   artist  had  made  a  mistake ;  they  were 
wrong.     When  it  was  explained,  some  agreed  and  some  dissented. 
Wanted,   immediately,  an    able    paradoxer :    testimonials    to  be 
forwarded  to  either  end  of  the  rainbow,  No.  1.     No  circle-squarer 
need    apply,  His    Variegatedness  having  been  pleased  to   adopt 
3' 141 59  .  .  .  from  Noah  downwards. 

The  system  of  Tycho  Brahe,  with  some  alteration  and  addition, 
has  been  revived  and  contended  for  in  our  own  day  by  a  Dane, 
W.  Zytphen,  who  has  published  '  The  Motion  of  the  Sun  in  the 
Universe,'  (second  edition)  Copenhagen,  1865,  8vo.,  and  '  Le 
Mouvement  Sideral,'  1 865,  8vo.  I  make  an  extract. — 

'  How  can  one  explain  Copernically  that  the  velocity  of  the  Moon 
must  be  added  (o  the  velocity  of  the  Earth  on  the  one  place  in  the 
Enrth's  orbit,  to  learn  how  far  the  Moon  has  advanced  from  one  fixed 
star  to  another  ;  but  in  another  place  in  the  orbit  these  velocities  must 
be  subtracted  (the  movements  taking  place  in  opposite  directions)  to 


472  A   BUDGET   OF  PARADOXES. 

attain  the  same  result  ?  In  the  Copernican  and  other  systems,  it  is 
well  known  that  the  Moon,  abstracting  from  the  insignificant  excen- 
tricity  of  the  orbit,  always  in  twenty-four  hours  performs  an  equally 
long  distance.  Why  has  Copernicus  never  been  denominated  Funda- 
mentus  or  Fundator  ?  Because  he  has  never  convinced  anybody  so 
thoroughly  that  this  otherwise  so  natural  epithet  has  occurred  to  the 
mind.' 

Eeally  the  second  question  is  more  effective  against  Newton 
than  against  Copernicus  ;  for  it  upsets  gravity :  the  first  is  of 
great  depth. 

The  Correspondent  journal  makes  a  little  episode  in  the  history 
of  my  Budget  (born  May,  1865,  died  April,  1866).  It  consisted 
entirely  of  letters  written  by  correspondents.  In  August,  a  cor- 
respondent who  signed  '  Fair  Play ' — and  who  I  was  afterwards 
told  was  a  lady — thought  it  would  be  a  good  joke  to  bring  in  the 
Cyclometers.  Accordingly  a  letter  was  written,  complaining  that 
though  Mr.  Sylvester's  demonstration  of  Newton's  theorem — then 
attracting  public  attention — was  duly  lauded,  the  possibly  greater 
discovery  of  the  quadrature  seemed  to  be  blushing  unseen,  and 
wasting  &c.  It  went  on  as  follows : — 

'  Prof.  De  Morgan,  who,  from  his  position  in  the  scientific  world, 
might  fairly  afford  to  look  favourably  on  less  practised  efforts  than  his 
own,  seems  to  delight  in  ridiculing  the  discoverer.  Science  is,  of 
course,  a  very  respectable  person  when  he  comes  out  and  makes  him- 
self useful  in  the  world  [it  must  have  been  a  lady ;  each  sex  gives 
science  to  the  other]  :  but  when,  like  a  monk  of  the  Middle  Ages,  he 
shuts  himself  up  [it  must  have  been  a  lady  ;  they  always  snub  the 
bachelors]  in  his  cloistered  cell,  repeating  his  mumpsimus  from  day 
to  day,  and  despising  the  labourers  on  the  outside,  we  begin  to  think 
of  Galileo,  Jenner,  Harvey,  and  other  glorious  trios,  who  have  been 
contemned  .  .  .' 

The  writer  then  called  upon  Mr.  James  Smith  to  come  forward. 
The  irony  was  not  seen ;  and  that  day  fortnight  appeared  the 
first  of  more  than  thirty  letters  from  his  pen.  Mr.  Smith  was 
followed  by  Mr.  Eeddie,  Zadkiel,  and  others,  on  their  several 
subjects.  To  some  of  the  letters  I  have  referred ;  to  otbers  I 
shall  come.  The  Correspondent  was  to  become  a  first-class 
scientific  journal;  the  time  had  arrived  at  which  truth  had. an 
organ  :  and  I  received  formal  notice  that  I  could  not  stifle  it  by 
silence,  nor  convert  it  into  falsehood  by  ridicule.  When  my 
reader  sees  my  extracts,  be  will  readily  believe  my  declaration 
that  I  should  have  been  the  last  to  stifle  a  publication  which  was 
every  week  what  James  Mill  would  call  a  dose  of  capital  for  my 


LETTER   TO   ATHEN^UM.  478 

Budget.  A  few  anti-paradoxers  brought  in  common  sense :  but 
to  the  mass  of  the  readers  of  the  journal  it  all  seemed  to  be 
the  difference  between  Tweedledum  and  Tweedledee.  Some  said 
that  the  influx  of  scientific  paradoxes  killed  the  journal :  but  my 
belief  is  that  they  made  it  last  longer  than  it  otherwise  would 
have  done.  Twenty  years  ago  I  recommended  the  paradoxers  to 
combine  and  publish  their  views  in  a  common  journal :  with  a 
catholic  editor,  who  had  no  pet  theory,  but  a  stern  determination 
not  to  exclude  anything  merely  for  absurdity.  I  suspect  it  would 
answer  very  well.  A  strong  title,  or  motto,  would  be  wanted  :  not 
quite  so  coarse  as  was  roared  out  in  a  Cambridge  mob  when  I  was 
an  undergraduate — *  No  King  !  No  Church  !  No  House  of  Lords  ! 
No  nothing,  blast  me  ! ' —  but  something  on  that  principle. 

At  the  end  of  1867  I  addressed  the  following  letter  to  the 
Athenaeum, : — 

PSEUDOMATH,   PHILOMATH,   AND    GEAPHOMATH. 

December  31,  1867. 

MANY  thanks  for  the  present  of  Mr.  James  Smith's  letters  of  Sept.  28 
and  of  Oct.  10  and  12.  He  asks  where  you  will  be  if  yon  read  and 
digest  his  letters  :  you  probably  will  be  somewhere  first.  He  after- 
wards asks  what  the  WE  of  the  Athenceum  will  be  if,  finding  it  im- 
possible to  controvert,  it  should  refuse  to  print.  I  answer  for  you, 
that  We-We  of  the  Athenoeutn^  not  being  Wa-Wa  the  wild  goose,  so 
conspicuous  in  '  Hiawatha,'  will  leave  what  controverts  itself  to  print 
itself,  if  it  please. 

Philomath  is  a  good  old  word,  easier  to  write  and  speak  than 
mathematician.  It  wants  the  words  between  which  I  have  placed  it. 
They  are  not  well  formed ;  pseudomathetc.  and  graplwmathde  would  be 
better  :  but  they  will  do.  I  give  an  instance  of  each. 

The  pseudomath  is  a  person  who  handles  mathematics  as  the  monkey 
handled  the  razor.  The  creature  tried  to  shave  himself  as  he  had. 
peen  his  master  do  ;  but,  not  having  any  notion  of  the  angle  at  which 
the  razor  was  to  be  held,  lie  cut  his  own  throat.  He  never  tried  a 
second  time,  poor  animal  1  but  the  pseudomath  keeps  on  at  his  work, 
proclaims  himself  clean-shaved,  and  all  the  rest  of  the  world  hairy. 
So  great  is  the  difference  between  moral  and  physical  phenomena  ! 
Mr.  James  Smith  is,  beyond  doubt,  the  great  pseudomath  of  our  time. 
His  3^  is  the  least  of  a  wonderful  chain  of  discoveries.  His  books,  like 
Whitbread's  barrels,  will  one  day  reach  from  Simpkin  &  Marshall's  to 
Kew,  placed  upright,  or  to  Windsor  laid  lengthways.  The  Queen 
will  run  away  on  their  near  approach,  as  Bishop  Hatto  did  from  the 
rats  :  but  Mr.  James  Smith  will  follow  her  were  it  to  John  o'  Groats. 

The  philomath,  for  my  present  purpose,  must  be  exhibited  as  giving 


474  A   BUDGET   OF  PARADOXES. 

a  lesson  to  presumption.  The  following  anecdote  is  found  in  Thiebault's 
'  Souvenirs  de  vingt  ans  de  sejour  a  Berlin,'  published  in  1804.  The 
book  itself  got  a  high  character  for  truth.  In  1807  Marshal  Mollen- 
dorff  answered  an  inquiry  of  the  Due  de  Bassano,  by  saying  that  it 
was  the  most  veracious  of  books,  written  by  the  most  honest  of  men. 
Thiebault  does  not  claim  personal  knowledge  of  the  anecdote,  but 
he  vouches  for  its  being  received  as  true  all  over  the  north  of 
Europe.1 

Diderot  paid  a  visit  to  Russia  at  the  invitation  of  Catherine  the 
Second.  At  that  time  he  was  an  atheist,  or  at  least  talked  atheism  : 
it  would  be  easy  to  prove  him  either  one  thing  or  the  other  from  his 
writings.  His  lively  sallies  on  this  subject  much  amused  the  Empress, 
and  all  the  younger  part  of  her  Court.  But  some  of  the  older  courtiers 
suggested  that  it  was  hardly  prudent  to  allow  such  unreserved  ex- 
hibitions. The  Empress  thought  so  too,  but  did  not  like  to  muzzle 
her  guest  by  an  express  prohibition  :  so  a  plot  was  contrived.  The 
scorner  was  informed  that  an  eminent  mathematician  had  an  algebra- 
ical proof  of  the  existence  of  God,  which  he  would  communicate  before 
the  whole  Court,  if  agreeable.  Diderot  gladly  consented.  The  ma- 
thematician, who  is  not  named,  was  Euler.  He  came  to  Diderot  with 
the  gravest  air,  and  in  a  tone  of  perfect  conviction  said,  "  Monsieur! 


done  Dieu  existe  ;  repondez  \  "  Diderot,  to  whom  algebra  was  Hebrew, 
though  this  is  expressed  in  a  very  roundabout  way  by  Thiebault  —  and 
whom  we  may  suppose  to  have  expected  some  verbal  argument  of 
alleged  algebraical  closeness,  was  disconcerted  ;  while  peals  of  laughter 
sounded  on  all  sides.  Next  day  he  asked  permission  to  return  to 
France,  which  was  granted.  An  algebraist  would  have  turned  the 
tables  completely,  by  saying,  '  Monsieur  !  vous  savez  bien  que  votre 
raisonnement  demande  le  developpement  de  x  suivant  les  puissances 
entieres  de  %.'  Goldsmith  could  not  have  seen  the  anecdote,  or  he 
might  have  been  supposed  to  have  drawn  from  it  a  hint  as  to  the  way 
in  which  the  Squire  demolished  poor  Moses. 

The  graphomath  is  a  person  who,  having  no  mathematics,  attempts 
to  describe  a  mathematician.  Novelists  perform  in  this  way  :  even 
Walter  Scott  now  and  then  burns  his  fingers.  His  dreaming  calcu- 
lator, Davy  Ramsay,  swears  '  by  the  bones  of  the  immortal  Napier.  ' 
Scott  thought  that  the  philomaths  worshipped  relics  :  so  they  do,  in 
one  sense.  Look  into  Hutton's  Dictionary  for  Napier's  Bones,  and 
you  shall  learn  all  about  the  little  knick-knacks  by  which  he  did 
multiplication  and  division.  But  never  a  bone  of  his  own  did  he 
contribute  ;  he  preferred  elephants'  tusks.  The  author  of  '  Headlong 

1  This  anecdote  is  printed  at  p.  251  ;  but  as  it  is  used  in  illustration  here,  and  is 
giyen  more  in  detail,  I  have  not  omitted  it.  —  En. 


LETTER   TO   ATHEN^UM.  475 

Hall '  makes  a  grand  error,  which  is  quite  high  science :  he  says .  that 
Laplace  proved  the  precession  of  the  equinoxes  to  be  a  periodical 
inequality.  He  should  have  said  the  variation  of  the  obliquity.  But 
the  finest  instance  is  the  following  : — Mr.  Warren,  in  his  well-wrought 
tale  of  the  martyr-philosopher,  was  incautious  enough  to  invent  the 
symbols  by  which  his  savant  satisfied  himself  Laplace  was  right  on  a 
doubtful  point.  And  this  is  what  he  put  together — 


-  3a2,       a         +  9  -  n  =  9,  n  x  log  e. 


Now,  to  Diderot  and  the  mass  of  mankind  this  might  be  Laplace  all 
over  :  and,  in  a  forged  note  of  Pascal,  would  prove  him  quite  up  to 
gravitation.  But  I  know  of  nothing  like  it,  except  in  the  lately 
received  story  of  the  American  orator,  who  was  called  on  for  some 
Latin,  and  perorated  thus  :  —  '  Committing  the  destiny  of  the  country 
to  your  hands,  Gentlemen,  I  may  without  fear  declare,  in  the  language 
of  the  noble  Roman  poet, 

E  pluribus  unum, 
Multum  in  parvo, 
Ultima  Thule, 
Sine  qua  non." 

But  the  American  got  nearer  to  Horace  than  the  martyr-philosopher 
to  Laplace.  For  all  the  words  are  in  Horace,  except  Thule,  which 
might  have  been  there.  But  CD  is  not  a  symbol  wanted  by  Laplace  ; 
nor  can  we  see  how  it  could  have  been  :  in  fact,  it  is  not  recognized 
in  algebra.  As  to  the  junctions,  &c.,  Laplace  and  Horace  are  about 
equally  well  imitated. 

Further  thanks  for  Mr.  Smith's  letters  to  you  of  Oct.  15,  18,  19,  28, 
and  Nov.  4,  15.  The  last  of  these  letters  has  two  curious  discoveries. 
First,  Mr.  Smith  declares  that  he  has  seen  the  editor  of  the  Athenaeum  : 
in  several  previous  letters  he  mentions  a  name.  If  he  knew  a  little 
of  journalism  he  would  be  aware  that  editors  are  a  peculiar  race, 
obtained  by  natural  selection.  They  are  never  seen,  even  by  their 
officials  ;  only  heard  down  a  pipe.  Secondly,  '  an  ellipse  or  oval  ' 
is  composed  of  four  arcs  of  circles.  Mr.  Smith  has  got  hold  of  the 
construction  I  was  taught,  when  a  boy,  for  a  pretty  four-arc  oval.  But 
my  teachers  knew  better  than  to  call  it  an  ellipse  :  Mr.  Smith  does 
not  ;  but  he  produces  from  it  such  confirmation  of  3^  as  would  con- 
vince any  honest  editor. 

Surely  the  cyclometer  is  a  Darwinite  development  of  a  spider,  who 
is  always  at  circles,  and  always  begins  again  when  his  web  is  brushed 
away.  He  informs  you  that  he  has  been  privileged  to  discover  truths 
unknown  to  the  scientific  world.  This  we  know  ;  but  he  proceeds  to 
show  that  he  is  equally  fortunate  in  art.  He  goes  on  to  say  that  he 
will  make  use  of  you  to  bring  those  truths  to  light,  'just  as  an  artist 
makes  use  of  a  dummy  for  the  purpose  of  arranging  his  drapery.'  The 


476  A  BUDGET   OF  PARADOXES. 

painter's  lay-figure  is  for  flowing  robes  ;  the  hairdresser's  dummy  is 
for  curly  locks.  Mr.  James  Smith  should  read  Sam  Weller's  pathetic 
story  of  the  '  four  wax  dummies.'  As  to  his  use  of  a  dummy,  it  is 
quite  correct.  When  I  was  at  University  College,  I  walked  one  day 
into  a  room  in  which  my  Latin  colleague  was  examining.  One  of  the 
questions  was,  '  Give  the  lives  and  fates  of  Sp.  Maelius  and  Sp. 
Cassius.'  Umph !  said  I,  surely  all  know  that  Spurius  Mselius  was 
whipped  for  adulterating  flour,  and  that  Spurius  Cassius  was  hanged 
for  passing  bad  money.  Now,  a  robe  arranged  on  a  dummy  would 
look  just  like  the  toga  of  Cassius  on  the  gallows.  Accordingly,  Mr. 
Smith  is  right  in  the  drapery-hanger  which  he  has  chosen :  he  has 
been  detected  in  the  attempt  to  pass  bad  circles.  He  complains 
bitterly  that  his  geometry,  instead  of  being  read  and  understood  by 
you,  is  handed  over  to  me  to  be  treated  after  my  scurrilous  fashion. 
It  is  clear  enough  that  he  would  rather  be  handled  in  this  way  than 
not  handled  at  all,  or  why  does  he  go  on  writing  ?  He  must  know  by 
this  time  that  it  is  a  part  of  the  institution  that  his  '  untruthful  and 
absurd  trash '  shall  be  distilled  into  mine  at  the  rate  of  about  3^  pages 
of  the  first  to  one  column  of  the  second.  Your  readers  will  never 
know  how  much  they  gain  by  the  process,  until  Mr.  James  Smith 
publishes  it  all  in  a  big  book,  or  until  they  get  hold  of  what  he  has 
already  published.  I  have  six  pounds  avoirdupois  of  pamphlets  and 
letters  ;  and  there  is  more  than  half  a  pound  of  letters  written  to  you 
in  the  last  two  months.  Your  compositor  must  feel  aggrieved  by  the 
rejection  of  these  clearly  written  documents,  without  erasures,  and  on 
one  side  only.  Your  correspondent  has  all  the  makings  of  a  good 
contributor,  except  knowledge  of  his  subject  and  sense  to  get  it.  He 
is,  in  fact,  only  a  mask  :  of  whom  the  fox 

0  quanta  species,  inquit,  cerebrum  non  habet. 

I  do  not  despair  of  Mr.  Smith  on  any  question  which  does  not  involve 
that  unfortunate  two-stick  wicket  at  which  he  persists  in  bowling. 
He  has  published  many  papers ;  he  has  forwarded  them  to  mathema- 
ticians :  and  "he  cannot  get  answers;  perhaps  not  even  readers.  Does 
he  think  that  he  would  get  more  notice  if  you  were  to  print  him  in 
your  journal  ?  Who  would  study  his  columns  ?  Not  the  mathema- 
tician, we  know ;  and  he  knows.  Would  others  ?  His  balls  are 
aimed  too  wide  to  be  blocked  by  any  one  who  is  near  the  wicket.  He 
has  long  ceased  to  be  worth  the  answer  which  a  new  invader  may  get. 
Rowan  Hamilton,  years  ago,  completely  knocked  him  over ;  and  he 
has  never  attempted  to  point  out  any  error  in  the  short  and  easy 
method  by  which  that  powerful  investigator  condescended  to  show 
that,  be  right  who  may,  he  must  be  wrong.  There  are  some  persons 
who  feel  inclined  to  think  that  Mr.  Smith  should  be  argued  with :  let 
those  persons  understand  that  he  has  been  argued  with,  refuted,  and 
has  never  attempted  to  stick  a  pen  into  the  refutation.  He  stated 


MR.   EEDDIFS   ASTRONOMY.  477 

that  it  was  a  remarkable  paradox,  easily  explicable ;  and  that  is  all. 
After  this  evasion,  Mr.  James  Smith  is  below  the  necessity  of  being 
told  that  he  is  unworthy  of  answer.  His  friends  complain  that  I  do 
nothing  but  cliaff  him.  Absurd !  I  winnow  him ;  and  if  nothing  but 
chaff  results,  whose  fault  is  that  ?  I  am  usefully  employed  ;  for  he  is 
the  type  of  a  class  which  ought  to  be  known,  and  which  I  have  done 
much  to  make  known. 

Nothing  came  of  this  until  July  1869,  when  I  received  a 
reprint  of  the  above  letter^  with  a  comment,  described  as  Ap- 
pendix D  of  a  work  in  course  of  publication  on  the  geometry  of 
the  circle.  The  Athenoeum  journal  received  the  same  :  but  the 
Editor,  in  his  private  capacity,  received  the  whole  work,  being 
'  The  Geometry  of  the  Circle  and  Mathematics  as  applied  to 
Geometry  by  Mathematicians,  shown  to  be  a  mockery,  delusion, 
and  a  snare,'  Liverpool,  8vo.,  1869.  Mr.  J.  S.  here  appears  in 
deep  fight  with  Prof.  Whitworth,  and  Mr.  Wilson,  the  author  of 
the  alleged  amendment  of  Euclid.  How  these  accomplished 
mathematicians  could  be  inveigled  into  continued  discussion  is 
inexplicable.  Mr.  Whitworth  began  by  complaining  of  Mr. 
Smith's  attacks  upon  mathematicians,  continued  to  correspond 
after  he  was  convinced  that  J.  S.  proved  an  arc  and  its  chord 
to  be  equal,  and  only  retreated  when  J.  S.  charged  him  with 
believing  in  3£,  and  refusing  acknowledgment.  Mr.  Wilson  was 
introduced  to  J.  S.  by  a  volunteer  defence  of  his  geometry  from 
the  assaults  of  the  Athenceum.  This  the  editor  would  not 
publish ;  so  J.  S.  sent  a  copy  to  Mr.  Wilson  himself.  Some 
correspondence  ensued,  but  Mr.  Wilson  soon  found  out  his  man, 
and  withdrew. 

There  is  a  little  derision  of  the  Athenceum  and  a  merited 
punishment  for  'that  unscrupulous  critic  and  contemptible 
mathematical  twaddler,  De  Morgan.' 

At  p.  371  I  mentioned  Mr.  Reddie,  the  author  of  Vis  Inert '/'<'• 
Victa  and  of  Victoria  tolo  ccelo,  which  last  is  not  an  address  to 
the  whole  heaven,  either,  from  a  Roman  Goddess  or  a  British 
Queen,  whatever  a  scholar  may  suppose.  Between  these  Mr. 
Reddie  has  published  'The  Mechanics  of  the  Heavens,'  8vo., 
1862  :  this  I  never  saw  until  he  sent  it  to  me,  with  an  invitation 
to  notice  it,  he  very  well  knowing  what  it  would  catch.  His  spe- 
culations do  battle  with  common  notions  of  mathematics  and  of 
mechanics,  which,  to  use  a  feminine  idiom,  he  blasphemes  so  you 
can't  think  !  and  I  suspect  that  if  you  do  not  blaspheme  them  too, 
you  can't  think.  He  appeals  to  the  'truly  scientific,'  and  would 


478  A   BUDGET  OF  PARADOXES. 

be  glad  to  have  readers  who  have  read  what  he  controverts,  i.  e. 
Newton's  Principia  :  I  wish  he  may  get  them ;  I  mean  I  hope  he 
may  obtain  them.  To  none  but  these  would  an  account  of  his 
speculations  be  intelligible  :  I  accordingly  disposed  of  him  in  a 
very  short  paragraph  of  description.  Now  many  paradoxefs 
desire  notice,  even  though  it  be  disparaging.  I  have  letters  from 
more  than  one — besides  what  have  been  sent  to  the  Editor  of  the 
Athenaeum — complaining  that  they  are  not  laughed  at ;  although 
they  deserve  it,  they  tell  me,  as  much  as  some  whom  I  have 
inserted.  Mr.  Reddie  informs  me  that  I  have  not  said  a  single 
word  against  his  books,  though  I  have  given  nearly  a  column  to 
sixteen-string  arithmetic,  and  as  much  to  animalcule  universes. 
What  need  to  say  anything  to  readers  of  Newton  against  a  book 
from  which  I  quoted  that  revolution  by  gravitation  is  demon- 
strably  impossible  ?  It  would  be  as  useless  as  evidence  against  a 
man  who  has  pleaded  guilty.  Mr.  Reddie  derisively  thanks  me 
for  '  small  mercies  ' ;  he  wrote  me  private  letters  ;  he  published 
them,  and  more,  in  the  Correspondent.  He  gave  me,  pro 
virlbus  suis,  such  a  dressing  you  can't  think,  both  for  my  Budget 
non-notice,  and  for  reviews  which  he  assumed  me  to  have  written. 
He  outlawed  himself  by  declaring  (Correspondent,  Nov.  11, 1856) 
that  I — in  a  review — had  made  a  quotation  which  was  '  garbled, 
evidently  on  purpose  to  make  it  appear  that '  he  '  was  advocating 
solely  a  geocentric  hypothesis,  which  is  not  true.'  In  fact,  he  did 
his  very  best  to  get  larger  'mercy.'  And  he  shall  have  it;  and  at 
a  length  which  shall  content  him,  unless  his  mecometer  be  an 
insatiable  apparatus.  But  I  fear  that  in  other  respects  I  shall  no 
more  satisfy  him  than  the  Irish  drummer  satisfied  the  poor 
culprit  when,  after  several  times  changing  the  direction  of  the 
stroke  at  earnest  entreaty,  he  was  at  last  provoked  to  call  out, 
*  Bad  cess  to  ye,  ye  spalpeen !  strike  where  one  will,  there  's  no 
placing  ye ! ' 

Mi\  Reddie  attaches  much  force  to  Berkeley's  old  arguments 
against  the  doctrine  of  fluxions,  and  advances  objections  to 
Newton's  second  section^  which  he  takes  to  be  new.  To  me  they 
appear  '  such  as  have  been  often  made,'  to  copy  a  description 
given  in  a  review :  though  I  have  no  doubt  Mr.  Reddie  got  them 
out  of  himself.  But  the  whole  matter  comes  to  this  :  Mr.  Reddie 
challenged  answer,  especially  from  the  British  Association,  and  got 
none.  He  presumes  that  this  is  because  he  is  right,  and  cannot 
be  answered  :  the  Association  is  willing  to  risk  itself  upon  the 
counter-notion  that  he  is  wrong,  and  need  not  be  answered ; 


MR.   REDDIFS   ASTRONOMY.  479 

because  so  wrong  that  none  who  could  understand  an  answer 
would  be  likely  to  want  one. 

Mr.  Eeddie  demands  my  attention  to  a  point  which  had 
already  particularly  struck  me,  as  giving  the  means  of  showing 
to  all  readers  the  kind  of  confusion  into  which  paradoxers  are  apt 
to  fall,  in  spite  of  the  clearest  instruction.  It  is  a  very  honest 
blunder,  and  requires  notice :  it  may  otherwise  mislead  some, 
who  may  suppose  that  no  one  able  to  read  could  be  mistaken 
about  so  simple  a  matter,  let  him  be  ever  so  wrong  about  New- 
ton. According  to  his  own  mis-statement,  in  less  than  five 
months  he  made  the  Astronomer  Eoyal  abandon  the  theory  of 
the  solar  motion  in  space.  The  announcement  is  made  in 
August,  1865,  as  follows  :  the  italics  are  not  mine  : — 

'  The  third  (Victoria  .  .  .),  although  only  published  in  September, 
1863,  has  already  had  its  triumph.  It  is  the  book  that  forced  the  As- 
tronomer Royal  of  England,  after  publicly  teaching  the  contrary  for  years, 
to  come  to  the  conclusion^  "strange  as  it  may  appear,"  that  "the  ^vhole 
question  of  solar  motion  in  space  is  at  the  present  time  in  doubt  and  abey- 
ance." This  admission  is  made  in  the  Annual  Report  of  the  Council 
of  the  Royal  Astronomical  Society,  published  in  the  Society's  Monthly 
Notices  for  February,  1864.' 

It  is  added  that  solar  motion  is  <  full  of1  self-contradiction, 
which  "  the  astronomers  "  simply  overlooked,  but  which  they  dare 
not  now  deny  after  being  once  pointed  out.' 

The  following  is  another  of  his  accounts  of  the  matter,  given  in 
the  Correspondent,  Nov.  18,  1865  : — 

' .  .  .  You  ought,  when  you  came  to  put  me  in  the  "  Budget,"  to 
have  been  aware  of  the  Report  of  the  Council  of  the  Royal  Astronomical 
Society,  where  it  appears  that  Professor  Airy,  with  a  better  appreci- 
ation of  my  demonstrations,  had  admitted — "  strange,"  say  the  Council, 
"  as  it  may  appear  " — that  "  the  whole  question  of  solar  motion  in 
space  [and  here  Mr.  Reddie  omits  some  words]  is  now  in  doubt  and 
abeyance"  You  were  culpable,  as  a  public  teacher  of  no  little  pre- 
tensions, if  you  were  "  unaware  "  of  this.  If  aware  of  it,  you  ought  not 
to  have  suppressed  such  an  important  testimony  to  my  really  having 
been  "very  successful"  in  drawing  the  teeth  of  the  pegtops,  though 
you  thought  them  so  firmly  fixed.  And  if  you  still  suppress  it,  in  your 
Appendix,  or  when  you  reprint  your  "  Budget,"  you  will  then  be  guilty 
of  a  sttppressio  veri,  also  of  further  injury  to  me,  who  have  never  in- 
jured you  .  .  .' 

Mr.  Reddie  must  have  been  very  well  satisfied  in  his  own  mind 
before  he  ventured  such  a  challenge,  with  an  answer  from  me 


480  A  BUDGET   OF  PARADOXES. 

looming  in  the  distance.     The  following  is  the  passage  of  the 
Eeport  of  the  Council,  &c.,  from  which  he  quotes : — 

'  And  yet,  strange  to  say,  notwithstanding  the  near  coincidence  of 
all  the  results  of  the  before-mentioned  independent  methods  of  investi- 
gation, the  inevitable  logical  inference  deduced  by  Mr.  Airy  is,  that 
the  whole  question  of  solar  motion  in  space,  so  far  at  least  as  accounting 
for  the  proper  motion  of  the  stars  is  concerned,  [I  have  put  in  italics  the 
words  omitted  by  Mr.  Reddie]  appears  to  remain  at  this  moment  iu 
doubt  and  abeyance.' 

Mr.  Reddie  has  forked  me,  as  he  thinks,  on  a  dilemma  :  if 
unaware,  culpable  ignorance ;  if  aware,  suppressive  intention. 
But  the  thing  is  a  trilemma,  and  the  third  horn,  on  which  I 
elect  to  be  placed,  is  surmounted  by  a  doubly-stuffed  seat.  First, 
Mr.  Airy  has  not  changed  his  opinion  about  the  fact  of  solar 
motion  in  space,  but  only  suspends  it  as  to  the  sufficiency  of 
present  means  to  give  the  amount  and  direction  of  the  motion. 
Secondly,  all  that  is  alluded  to  in  the  Astronomical  Report  was 
said  and  printed  before  the  Victoria  proclamation  appeared.  So 
that  the  author,  instead  of  drawing  the  tooth  of  the  Astronomer 
Royal's  pegtop,  has  burnt  his  own  doll's  nose. 

William  Herschel,  and  after  him  about  six  other  astronomers, 
had  aimed  at  determining,  by  the  proper  motions  of  the  stars, 
the  point  of  the  heavens  towards  which  the  solar  system  is 
moving :  their  results  were  tolerably  accordant.  Mr.  Airy,  in 
1859,  proposed  an  improved  method,  and,  applying  it  to  stars  of 
large  proper  motion,  produced  much  the  same  result  as  Herschel. 
Mr.  E.  Dunkin,  one  of  Mr.  Airy's  staff  at  Greenwich,  applied  Mr. 
Airy's  method  to  a  very  large  number  of  stars,  and  produced, 
again,  nearly  the  same  result  as  before.  This  paper  was  read 
to  the  Astronomical  Society  in  March,  1863,  was  printed  in 
abstract  in  the  Notice  of  that  month,  was  printed  in  full  in  the 
volume  then  current,  and  was  referred  to  in  the  Annual  Report 
of  the  Council  in  February,  1864,  under  the  name  of  'the 
Astronomer  Royal's  elaborate  investigation,  as  exhibited  by  Mr. 
Dunkin.'  Both  Mr.  Airy  and  Mr.  Duiikin  express  grave  doubts 
as  to  the  sufficiency  of  the  data  :  and,  regarding  the  coincidence 
of  all  the  results  as  highly  curious,  feel  it  necessary  to  wait  for 
calculations  made  on  better  data.  The  report  of  the  Council 
states  these  doubts.  Mr.  Reddie,  who  only  published  in  Sep- 
tember, 1863,  happened  to  see  the  Report  of  February,  1864, 
assumes  that  the  doubts  were  then  first  expressed,  and  declares 
that  his  book  of  September  had  the  triumph  of  forcing  the 


MR.   REDDIE   AXD   THE   ASTRONOMER   ROYAL.  481 

Astronomer  Royal  to  abandon  the  fact  of  motion  of  the  solar 
system  by  the  February  following.  Had  Mr.  Reddie,  when  he 
saw  that  the  Council  were  avowedly  describing  a  memoir  pre- 
sented some  time  before,  taken  the  precaution  to  rind  out  when 
that  memoir  was  presented,  he  would  perhaps  have  seen  that 
doubts  of  the  results  obtained,  expressed  by  one  astronomer  in 
March,  1863,  and  by  another  in  1859,  could  not  have  been  due 
to  his  publication  of  September,  1863.  And  any  one  else  would 
have  learnt  that  neither  astronomer  doubts  the  solar  motion, 
though  both  doubt  the  sufficiency  of  present  means  to  determine 
its  amount  and  direction.  This  is  implied  in  the  omitted 
words,  which  Mr.  Reddie — whose  omission  would  have  been 
dishonest  if  he  had  seen  their  meaning — no  doubt  took  for 
pleonasm,  superfluity,  overmuchness.  The  rashness  which  pushed 
him  headlong  into  the  quillet  that  his  thunderbolt  had  stopped 
the  chariot  of  the  Sun  and  knocked  the  Greenwich  Phaethon  off 
the  box,  is  the  same  which  betrayed  him  into  yet  grander  error — 
which  deserves  the  full  word,  quidlibet — about  the  Principia  of 
Newton.  There  has  been  no  change  of  opinion  at  all.  When 
a  person  undertakes  a  long  investigation,  his  opinion  is  that, 
at  a  certain  date,  there  is  primd  facie  ground  for  thinking  a 
sound  result  may  be  obtained.  Should  it  happen  that  the  in- 
vestigation ends  in  doubt  upon  the  sufficiency  of  the  grounds, 
the  investigator  is  not  put  in  the  wrong.  He  knew  beforehand 
that  there  was  an  alternative :  and  he  takes  the  horn  of  the 
alternative  indicated  by  his  calculations.  The  two  sides  of  this 
case  present  an  instructive  contrast.  Eight  astronomers  produce 
nearly  the  same  result,  and  yet  the  last  two  doubt  the  sufficiency 
of  their  means  :  compare  them  with  the  what's-his-name  who 
rushes  in  where  thing-em-bobs  fear  to  tread. 

I  was  not  aware,  until  what  I  had  written  what  precedes,  that 
Mr.  Airy  had  given  a  sufficient  answer  on  the  point.  Mr.  Reddie 
says  (Correspondent,  Jan.  20,  1866): — 

'  I  claim  to  have  forced  Professor  Airy  to  give  up  the  notion  of 
"  solar  motion  in  space  "  altogether,  for  he  admits  it  to  be  "at  present 
in  doubt  and  abeyance."  I  first  made  that  claim  in  a  letter  addressed 
to  the  Astronomer  Royal  himself  in  June,  1864,  and  in  replying,  very 
courteously,  to  other  portions  of  my  letter,  he  did  not  gainsay  that 
part  of  it.' 

Mr.  Reddie  is  not  ready  at  reading  satire,  or  he  never  would 
have  so  missed  the  meaning  of  the  courteous  reply  on  one  point, 
and  the  total  silence  upon  another.  Mr.  Airy  must  be  one  of 

I  i 


482  A  BUDGET   OF  PARADOXES. 

those  peculiar  persons  who,  when  they  do  not  think  an  assertion 
worth  notice,  let  it  alone,  without  noticing  it  by  a  notification 
of  non-notice.  He  would  never  commit  the  bull  of  '  Sir  !  I  will 
not  say  a  word  on  that  subject.'  He  would  put  it  thus,  '  Sir!  I 
will  only  say  ten  words  on  that  subject,' — and,  having  thus  said 
them,  would  proceed  to  something  else.  He  assumed,  as  a  matter 
of  form,  that  Mr.  Reddie  would  draw  the  proper  inference  from 
his  silence :  and  this  because  he  did  not  care  whether  or  no  the 
assumption  was  correct. 

The  '  Mechanics  of  the  Heavens,'  which  Mr.  Reddie  sends  to  be 
noticed,  shall  be  noticed,  so  far  as  an  extract  goes  :— 

'  My  connexion  with  this  subject  is,  indeed,  very  simply  explained. 
In  endeavouring  to  understand  the  laws  of  physical  astronomy  as 
generally  taught,  I  happened  to  entertain  some  doubt  whether  gravi- 
tating bodies  could  revolve,  and  having  afterwards  imbibed  some  vague 
idea  that  the  laws  of  the  universe  were  chemical  and  physical  rather 
than  mechanical,  and  somehow  connected  with  electricity  and  mag- 
netism as  opposing  and  correlative  forces — most  probably  suggested  to 
my  mind,  as  to  many  others,  by  the  transcendent  discoveries  made  in 
electro-magnetism  by  Professor  Faraday — my  former  doubts  about 
gravitation  were  revived,  and  I  was  led  very  naturally  to  try  and  dis- 
cover whether  a  gravitating  body  really  could  revolve ;  and  I  became 
convinced  it  could  not,  before  I  had  ever  presumed  to  look  into  the 
demonstrations  of  the  Principia.' 

This  is  enough  against  the  book,  without  a  word  from  me  :  I 
insert  it  only  to  show  those  who  know  the  subject  what  manner  of 
writer  Mr.  Reddie  is.  It  is  clear  that  '  presumed  '  is  a  slip  of  the 
pen  ;  it  should  have  been  condescended. 

Mr.  Reddie  represents  me  as  dreaming  over  paltry  paradoxes. 
He  is  right ;  many  of  my  paradoxes  are  paltry :  he  is  wrong ; 
I  am  wide  awake  to  them.  A  single  moth,  beetle,  or  butterfly, 
may  be  a  paltry  thing ;  but  when  a  cabinet  is  arranged  by  genus 
and  species,  we  then  begin  to  admire  the  infinite  variety  of  a 
system  constructed  on  a  wonderful  sameness  of  leading  character- 
istics. And  why  should  paradoxes  be  denied  that  collective  im- 
portance, paltry  as  many  of  them  may  individually  be,  which  is 
accorded  to  moths,  beetles,  or  butterflies  ?  Mr.  Reddie  himself 
sees  that  '  there  is  a  method  in '  my  { mode  of  dealing  with  para- 
doxes.' I  hope  I  have  atoned  for  the  scantiness  of  my  former 
article,  and  put  the  demonstrated  impossibility  of  gravitation  on 
that  level  with  Hubongramillposanfy  arithmetic  and  inhabited 
atoms  which  the  demonstrator — not  quite  without  reason — claims 
for  it. 


MR.   REDDIF/S   CHALLKN*  i  K.  483 

In  the  Introduction  to  a  collected  edition  of  the  three  works, 
Mr.  Reddie  describes  his  Mechanism  of  the  Heavens,  from  which 
I  have  just  quoted,  as — 

'  a  public  challenge  offered  to  the  British  Association  and  the  mathe- 
maticians at  Cambridge,  in  August,  1862,  calling  upon  them  to  point 
to  a  single  demonstration  in  the  Principia  or  elsewhere,  which  even 
attempts  to  prove  that  Universal  Gravitation  is  possible,  or  to  show 
that  a  gravitating  body  could  possibly  revolve  about  a  centre  of 
attraction.  The  challenge  was  not  accepted,  and  never  will  be.  No 
such  demonstration  exists.  And  the  public  must  judge  for  themselves 
as  to  the  character  of  a  so-called  "certain  science,"  which  thus  shrinks 
from  rigid  examination,  and  dares  not  defend  itself  when  publicly 
attacked :  also  of  the  character  of  its  teachers,  who  can  be  content  to 
remain  dumb  under  such  circumstances.' 

The  above  is  the  commonplace  talk  of  the  class,  of  which  I 
proceed  to  speak  without  more  application  to  this  paradoxer  than 
to  that.     It  reminds  one  of  the  funny  young  rascals  who  used,  in 
times  not  yet  quite  forgotten,  to  abuse  the  passengers,  as  long  as 
they  could  keep  up  with  the  stage  coach  ;  dropping  off  at  last 
with  '  Why  don't  you  get  down  and  thrash  us  ?     You're  afraid, 
you're  afraid ! '     They  will  allow  the  public  to  judge  for  them- 
selves, but  with  somewhat  of  the  feeling  of  the  worthy  uncle  in 
Tom  Jones,  who,  though  he  would  let  young  people  choose  for 
themselves,  would  have  them  choose  wisely.     They  try  to  be  so 
awfully  moral  and  so  ghastly  satirical  that  they  must  be  answered : 
and  they  are  best  answered  in  their  own  division.     We  have  all 
heard  of  the  way  in  which  sailors  cat's-pawed  the  monkeys :  they 
taunted  the  dwellers  in  the  trees  with  stones,  and  the  monkeys 
taunted  them  with  cocoa-nuts  in  return.    But  these  were  silly  den- 
drobats :  had  they  belonged  to  the  British  Association  they  would 
have  said — No  !  No  I  dear  friends  ;  it  is  not  in  the  itinerary :  if 
you  want  nuts,  you  must  climb,  as  we  do.    The  public  has  referred 
the  question  to  Time  :  the  procedure  of  this  great  king  I  venture 
to  describe,  from  precedents,  by   an   adaptation  of  some  smart 
anapaestic  tetrameters — your  anapaest  is  the  foot  for  satire  to  halt 
on,  both  in  Greek  and  English — which  I  read  about  twenty  years 
ago,  and  with  the  point  of  which  I  was  much  tickled.     Poetasters 
were  laughed  at ;  but  Mr.  Slum,  whom  I  employed — Mr.  Charles 
Dickens  obliged  me  with  his  address — converted  the  idea  into  that 
of  a  hit  at  mathematicasters,  as  easily  as  he  turned  the  Warren 
acrostic  into  Jarley.     As  he  observed,  when   I  settled  his  little 
account,  it  is  cheaper  than  any  prose,  though  the  broom  was  not 
stolen  quite  ready  made  : — 


484  A  BUDGET  OF   PAKADOXES. 


Forty  stripes  save  one  for  the  smaller  Paradoxers. 

Hark  to  the  wisdom  the  sages  preach. 

Who  never  have  learnt  what  they  try  to  teach. 

We  are  the  lights  of  the  age,  they  say  ! 

We  are  the  men,  and  the  thinkers  we ! 

So  we  build  up  guess-work  the  livelong  day, 

In  a  topsy-turvy  sort  of  way, 

Some  with  and  some  wanting  a  plus  6. 

Let  the  British  Association  fuss  ; 

What  are  theirs  to  the  feats  to  be  wrought  by  us  ? 

Shall  the  earth  stand  still  ?    Will  the  round  come  square  ? 

Must  Isaac's  book  be  the  nest  of  a  mare  ? 

Ought  the  moon  to  be  taught  by  the  laws  of  space 

To  turn  half  round  without  right-about-face  ? 

Our  whimsey  crotchets  will  manage  it  all ; 

Deep  !  Deep  !  posterity  will  them  call ! 

Though  the  world,  for  the  present,  lets  them  fall 

Down  !  Down  !  to  the  twopenny  box  of  the  stall ! 

Thus  they — But  the  marplot  Time  stands  by, 
With  a  knowing  wink  in  his  funny  old  eye. 
He  grasps  by  the  top  an  immense  fool's  cap, 
Which  he  calls  a  philosophaster-trap : 
And  rightly  enough,  for  while  these  little  men 
Croak  loud  as  a  concert  of  frogs  in  a  fen, 
He  first  singles  out  one,  and  then  another, 
Down  goes  the  cap — lo  !  a  moment's  pother, 
A  spirt  like  that  which  a  rushlight  utters 
As  just  at  the  last  it  kicks  and  gutters  : 
When  the  cruel  smotherer  is  raised  again 
Only  snuff,  and  but  little  of  that,  will  remain. 

But  though  uno  avulso  thus  conies  every  day 

Non  deficit  alter  is  also  in  play : 

For  the  vacant  parts  are,  one  and  all, 

Soon  taken  by  puppets  just  as  small ; 

Who  chirp,  chirp,  chirp,  with  a  grasshopper  glee, 

We  're  the  lamps  of  the  Universe,  We  !  We !  We  ! 

But  Time,  whose  speech  is  never  long, — 

He  hasn't  time  for  it — stops  the  song 

And  says — Lilliput  lamps  !  leave  the  twopenny  boxes, 

And  shine  in  the  Budget  of  Paradoxes  ! 

When  a  paradoxer  parades  capital  letters  and  diagrams  which  are 
as  good  as  Newton's  to  all  who  know  nothing  about  it,  some  persons 


TIME   THE   SETTLER   OF   PARADOX.  485 

wonder  why  science  does  not  rise  and  triturate  the  whole  thing. 
This  is  why :  all  who  are  fit  to  read  the  refutation  are  satisfied 
already,  and  can,  if  they  please,  detect  the  paradoxer  for  themselves. 
Those  who  are  not  fit  to  do  this  would  not  know  the  difference  be- 
tween the  true  answer  and  the  new  capitals  and  diagrams  on  which 
the  delighted  paradoxer  would  declare  that  he  had  crumbled  the 
philosophers,  and  not  they  him.  Trust  him  for  having  the  last 
word :  and  what  matters  it  whether  he  crow  the  unanswerable 
sooner  or  later  ?  There  are  but  two  courses  to  take.  One  is  to 
wait  until  he  has  committed  himself  in  something  which  all  can 
understand,  as  Mr.  Keddie  has  done  in  his  fancy  about  the 
Astronomer  Royal's  change  of  opinion :  he  can  then  be  put  in  his 
true  place.  The  other  is  to  construct  a  Budget  of  Paradoxes,  that 
the  world  may  see  how  the  thing  is  always  going  on,  and  that  the 
picture  I  have  concocted  by  cribbing  and  spoiling  a  bit  of  poetry 
is  drawn  from  life.  He  who  wonders  at  there  being  no  answer 
has  seen  one  or  two  :  he  does  not  know  that  there  are  always  fifty 
with  equal  claims,  each  of  whom  regards  his  being  ranked  with 
the  rest  as  forty-nine  distinct  and  several  slanders  upon  himself, 
the  great  Mully  Ully  Gue.  And  the  fifty  would  soon  be  five 
hundred  if  any  notice  were  taken  of  them.  They  call  mankind 
to  witness  that  science  will  not  defend  itself,  though  publicly 
attacked  in  terms  which  might  sting  a  pickpocket  into  standing 
up  for  his  character :  science,  in  return,  allows  mankind  to  witness 
or  not,  at  pleasure,  that  it  does  not  defend  itself,  and  yet  receives 
no  injury  from  centuries  of  assault.  Demonstrative  reason  never 
raises  the  cry  of  Church  in  Danger !  and  it  cannot  have  any 
Dictionary  of  Heresies  except  a  Budget  of  Paradoxes.  Mistaken 
claimants  are  left  to  Time  and  his  extinguisher,  with  the  appro- 
bation of  all  thinking  non-claimants :  there  is  no  need  of  a  suc- 
cession of  exposures.  Time  gets  through  the  job  in  his  own  work- 
manlike manner,  as  already  described. 

On  looking  back  more  than  twenty  years,  I  find  among  my 
cuttings  the  following  passage,  relating  to  a  person  who  had 
signalized  himself  by  an  effort  to  teach  comets  to  the  conductor 
of  the  Nautical  Almanac : — 

'  Our  brethren  of  the  literary  class  have  not  the  least  idea  of  tlie 
small  amount  of  appearance  of  knowledge  which  sets  up  the  scientific 
charlatan.  Their  world  is  large,  and  there  are  many  who  have  that 
moderate  knowledge,  and  perception  of  what  is  knowledge,  before 
which  extreme  ignorance  is  detected  in  its  first  prank.  There  is  a 
public  of  moderate  cultivation,  for  the  most  part  sound  in  its  judgment, 
always  ready  in  its  decisions.  Accordingly,  all  their  successful  pre- 


486  A  BUDGET   OF  PABADOXES. 

tenders  have  some  pretension.  It  is  not  so  in  science.  Those  who  have 
a  right  to  judge  are  fewer  and  farther  between.  The  consequence  is, 
that  many  scientific  pretenders  have  nothing  but  pretension.' 

This  is  nearly  as  applicable  now  as  then.  It  is  impossible  to 
make  those  who  have  not  studied  for  themselves  fully  aware  of 
the  truth  of  what  I  have  quoted.  The  best  chance  is  collection 
of  cases ;  in  fact,  a  Budget  of  Paradoxes.  Those  who  have  no 
knowledge  of  the  subject  can  thus  argue  from  the  seen  to  the 
unseen.  All  can  feel  the  impracticability  of  the  Hubongra- 
millposanfy  numeration,  and  the  absurdity  of  the  equality  of 
contour  of  a  regular  pentagon  and  hexagon  in  one  and  the  same 
circle.  Many  may  accordingly  be  satisfied,  on  the  assurance  of 
those  who  have  studied,  that  there  is  as  much  of  impracticability, 
or  as  much  of  absurdity,  in  things  which  are  hidden  under 

Sines,  tangents,  secants,  radius,  cosines, 
Subtangents,  segments,  and  all  those  signs ; 
Enough  to  prove  that  he  who  read  'em 
Was  just  as  mad  as  he  who  made  'em. 

Not  that  I  mean  to  be  disrespectful  to  mathematical  terms : 
they  are  short  and  easily  explained,  and  compete  favourably  with 
those  of  most  other  subjects  :  for  instance,  with 

Horse-pleas,  traverses,  demurrers, 
Jeofails,  imparlances,  and  errors, 
Averments,  bars,  and  protestandos, 
And  puis  d'arreign  continuandos. 

From  which  it  appears  that,  taking  the  selections  made  by  satirists 
for  our  samples,  there  are,  one  with  another,  four  letters  more  in 
a  law  term  than  in  one  of  mathematics.  But  pleading  has  been 
simplified  of  late  years. 

All  paradoxers  can  publish ;  and  any  one  who  likes  may  read.  But 
this  is  not  enough ;  they  find  that  they  cannot  publish,  or  those 
who  can  find  they  are  not  read,  and  they  lay  their  plans  athwart 
the  noses  of  those  who,  they  think,  ought  to  read.  To  recom- 
mend them  to  be .  content  with  publication,  like  other  authors, 
is  an  affront :  of  this  I  will  give  the  reader  an  amusing  instance. 
My  good  nature,  of  which  I  keep  a  stock,  though  I  do  not  use  it 
all  up  in  this  Budget,  prompts  me  to  conceal  the  name. 

I  received  the  following  letter,  accompanied  by  a  prospectus  of 
a  work  on  metaphysics,  physics,  astronomy,  &c.  The  author  is 
evidently  one  whom  I  should  delight  to  honour  : — 


THE  BUDGETEER  CORRECTED.  487 

'  Sir, — A  friend  of  mine  has  mentioned  your  name  in  terms  of 
panigeric  [We],  as  being  of  high  standing  in  mathematics,  and  of 
greatly  original  thought.  I  send  you  the  enclosed  without  comment ; 
and,  assuming  that  the  bent  of  your  mind  is  in  free  inquiry,  shall  feel 
a  pleasure  in  showing  you  my  portfolio,  which,  as  a  mathematician, 
you  will  acknowledge  to  be  deeply  interesting,  even  in  an  educational 
point  of  view.  The  work  is  complete,  and  the  system  so  far  perfected 
as  to  place  it  above  criticism  ;  and,  so  far  as  regards  astronomy,  as 
will  Ptolemy  beyond  rivalry  [sic  :  no  doubt  some  words  omitted]. 
Believe  me  to  be,  Sir,  with  the  profoundest  respect,  &c.  The  work 
is  the  result  of  thirty-five  years'  travel  and  observation,  labour,  ex- 
pense, and  self-abnegation.' 

I  replied  to  the  effect  that  my  time  was  fully  occupied,  and 
that  I  was  obliged  to  decline  discussion  with  many  persons  who 
have  views  of  their  own ;  that  the  proper  way  is  to  publish,  so 
that  those  who  choose  may  read  when  they  can  find  leisure.  I 
added  that  I  should  advise  a  precursor  in  the  shape  of  a  small 
pamphlet,  as  two  octavo  volumes  would  be  too  much  for  most 
persons.  This  was  sound  advice ;  but  it  is  not  the  first,  second, 
or  third  time  that  it  has  proved  very  unpalatable.  I  received 
the  following  answer,  to  which  I  take  the  liberty  of  prefixing  a 
bit  of  leonine  wisdom  : — 

Si  doceas  stultum,  laetum  non  dat  tibi  vultum  ; 
Odit  te  multum ;  vellet  te  scire  sepultum. 

'  Sir, — I  pray  you  pardon  the  error  I  unintentionally  have  fallen 
into  ;  deceived  by  the  F.  R.  S.  [I  am  not  F.  R.  S.]  I  took  you  to  be 
a  man  of  science  [omnis  homo  est  animal,  Sortes  est  homo,  ergo  Sortes 
est  animal]  instead  of  the  mere  mathematician,  or  human  calculating- 
machine.  Believe  me,  Sir,  you  also  have  mistaken  your  mission,  as  I 
have  mine.  I  wrote  to  you  as  I  would  to  any  other  man  well  up  in 
mathematics,  with  the  intent  to  call  your  attention  to  a  singular  fact 
of  omission  by  Euclid,  and  other  great  mathematicians :  and,  in 
selecting  you,  I  did  you  an  honour  which,  from  what  I  have  just  now 
heard,  was  entirely  out  of  place.  I  think,  considering  the  nature  of 
the  work  set  forth  in  the  prospectus,  you  are  guilty  of  both  folly  and 
presumption,  in  assuming  the  character  of  a  patron  ;  for  your  own 
sense  ought  to  have  assured  you  that  was  such  my  object  I  should  not 
have  sought  him  in  a  De  Morgan,  who  exists  only  by  patronage  of 
others.  On  the  other  hand,  I  deem  it  to  be  an  unpardonable  piece  of 
presumption  in  offering  your  advice  upon  a  subject  the  magnitude, 
importance,  and  real  utility  of  which  you  know  nothing  about :  by 
doing  so  you  have  offered  me  a  direct  insult.  The  system  is  a  manual 
of  Philosophy,  a  one  inseparable  whole  of  metaphysics  and  physic  ; 


488  A   BUDGET   OF  PARADOXES. 

embracing  points  the  most  interesting,  laws  the  most  important,- 
doctrines  the  most  essential  to  advance  man  in  accordance  with  the 

spirit  of  the  times.     I  may  not  live  to  see  it  in  print ;  for,  at , 

life  at  best  is  uncertain  :  but,  live  or  die,  be  assured,  Sir,  it  is  not  my 
intention  to  debase  the  work  by  seeking  patronage,  or  pandering  to 
the  public  taste.  Your  advice  was  the  less  needed,  seeing  I  am  an 

old-established  .     I  remain,  &c. — P.  S.    You  will  oblige  me  by 

returning  the  prospectus  of  my  work.' 

My  reader  will,  I  am  sure,  not  take  this  transition  from  the 
*  profounclest  respect '  to  the  loftiest  insolence  for  an  apocraphi- 
cal  correspondence,  to  use  a  word  I  find  in  the  Prospectus :  on 
my  honour  it  is  genuine.  He  will  be  better  employed  in  dis- 
covering whether  I  exist  by  patronizing  others,  or  by  being 
patronized  by  them.  I  make  any  one  who  can  find  it  out  a  fair 
offer :  I  will  give  him  my  patronage  if  I  turn  out  to  be  Bufo,  on 
condition  he  gives  me  his,  if  I  turn  out  to  be  Bavius.  I  need 
hardly  say  that  I  considered  the  last  letter  to  be  one  of  those  to 
which  no  answer  is  so  good  as  no  answer. 

These  letters  remind  me  in  one  respect  of  the  correspondents 
of  the  newspapers.  My  other  party  wrote  because  a  friend  had 
pointed  me  out :  but  he  would  not  have  written  if  he  had  known 
what  another  friend  told  him  just  in  time  for  the  second  letter. 
The  man  who  sends  his  complaint  to  the  newspaper  very  often 
says,  in  effect,  '  Don't  imagine,  Sir,  that  I  read  your  columns  ; 
but  a  friend  who  sometimes  does  has  told  me  .  .  .  .  '  It  is  worded 
l,hus :  '  My  attention  has  been  directed  to  an  article  in  your 
paper  of  .  .  .  .'  Many  thanks  to  my  friend's  friends  for  not 
mentioning  the  Budget :  had  my  friend's  attention  been  directed 
to  it  I  might  have  lost  a  striking  example  of  the  paradoxer  in 
search  of  a  patron.  That  my  friend  was  on  this  scent  in  the  first 
letter  is  revealed  in  the  second.  Language  was  given  to  man  to 
conceal  his  thoughts ;  but  it  is  not  every  one  who  can  do  it. 

Among  the  most  valuable  information  which  my  readers  will 
get  from  me  is  comparison  of  the  reactions  of  paradoxers,  when 
not  admitted  to  argument,  or  when  laughed  at.  Of  course,  they 
are  misrepresented ;  and  at  this  they  are  angry,  or  which  is  the 
same  thing,  take  great  pains  to  assure  the  reader  that  they  are 
not.  So  far  natural,  and  so  far  good ;  anything  short  of  con- 
cession of  a  case  which  must  be  seriously  met  by  counter-reasons 
is  sure  to  be  misrepresentation.  My  friend  Mr.  James  Smith 
and  my  friend  Mr.  Reddie  are  both  terribly  misrepresented :  they 
resent  it  by  some  insinuations  in  which  it  is  not  easy  to  detect 
whether  I  am  a  conscious  smotherer  of  truth,  or  only  muddle- 


THE  DOUBLE   VAHU  PROt'Kss.  489 

headed  and  ignorant.  [This  was  written  before  I  received  my 
last  communication  from  Mr.  James  Smith.  He  tells  me  that  I  am 
wrong  in  saying  that  his  work  in  which  I  stand  in  the  pillory  is 
all  reprint  :  I  have  no  doubt  I  confounded  some  of  it  with  some 
of  the  manuscript  or  slips  which  I  had  received  from  my  much 
not-agreed-with  correspondent.  He  adds  that  my  mistake  was 
intentional,  and  that  my  reason  is  obvious  to  the  reader.  This  is 
information,  as  the  sea-serpent  said  when  he  read  in  the  news- 
paper that  he  had  a  mane  and  tusks.] 

My  friend  Dr.  Thorn  sees  deeper  into  my  mystery.  By  the  way, 
he  still  sends  an  occasional  touch  at  the  old  subject  ;  and  he  wants 
me  particularly  to  tell  my  readers  that  the  Latin  numeral  letters, 
if  M  be  left  out,  give  666.  And  so  they  do  :  witness  DCLXVI. 
A  person  who  thinks  of  the  origin  of  symbols  will  soon  see  that 
666  is  our  number  because  we  have  five  fingers  on  each  hand  : 
had  we  had  but  four,  our  mystic  number  would  have  been 
expressed  by  555,  and  would  have  stood  for  our  present  365. 
Had  n  been  the  number  on  each  hand,  the  great  number  would 
have  been 


With  no  finger  on  each  hand,  the  number  would  have  been  1  : 
with  one  finger  less  than  none  at  all  on  each  hand,  it  would  have 
been  0.  But  what  does  this  mean  ?  Here  is  a  question  for  an 
algebraical  paradoxer  !  So  soon  as  we  have  found  out  how  many 
fingers  the  inhabitants  of  any  one  planet  have  on  each  hand,  we 
have  the  means  of  knowing  their  number  of  the  Beast,  and 
thence  all  about  them.  Very  much  struck  with  this  hint  of  dis- 
covery, I  turned  my  attention  to  the  means  of  developing  it.  The 
first  point  was  to  clear  my  vision  of  all  the  old  cataracts.  I  propose 
.the  following  experiment,  subject  of  course  to  the  consent  of 
parties.  Let  Dr.  Thorn  Double-Vahu  Mr.  James  Smith,  and 
Thau  Mr.  Reddie  :  if  either  be  deparadoxed  by  the  treatment,  I 
will  consent  to  undergo  it  myself.  Provided  always  that  the 
temperature  required  be  not  so  high  as  the  Doctor  hints  at  :  if 
the  Turkish  Baths  will  do  for  this  world,  I  am  content. 

The  three  paradoxers  last  named  and  myself  have  a  pen- 
tasyllabic  convention,  under  which,  though  we  go  far  beyond 
civility,  we  keep  within  civilization.  Though  Mr.  James  Smitli 
pronounced  that  I  must  be  dishonest  if  I  did  not  see  his  argument, 
which  he  knew  I  should  not  do  [to  say  nothing  of  recent  accusa- 
tion] ;  though  Dr.  Thorn  declared  me  a  competitor  for  fire  and 
brimstone  —  and  my  wife,  too,  which  doubles  the  joke  :  though 


490  A   BUDGET   OF  PARADOXES. 

Mr.  Reddie  was  certain  I  had  garbled  him,  evidently  on  purpose 
to  make  falsehood  appear  truth  ;  yet  all  three  profess  respect  for 
me  as  to  everything  but  power  to  see  truth,  or  candour  to  admit 
it.  And  on  the  other  hand,  though  these  were  the  modes  of 
opening  communication  with  me,  and  though  I  have  no  doubt 
that  all  three  are  proper  persons  of  whom  to  inquire  whether  I 
should  go  up-stairs  or  down-stairs,  &c.,  yet  I  am  satisfied  they  are 
thoroughly  respectable  men,  as  to  everything  but  reasoning.  And 
I  dare  say  our  several  professions  are  far  more  true  in  extent  than 
in  many  which  are  made  under  more  parliamentary  form.  We 
find  excuses  for  each  other :  they  make  allowance  for  my  being 
hoodwinked  by  Aristotle,  by  Newton,  by  the  Devil  ;  and  I  permit 
them  to  feel,  for  I  know  they  cannot  get  on  without  it,  that  their 
reasons  are  such  as  none  but  a  knave  or  a  sinner  can  resist.  But 
they  are  content  with  cutting  a  slice  each  out  of  my  character : 
neither  of  them  is  more  than  an  uncle,  a  Bone-a-part ;  I  now  come 
to  a  dreadful  nephew,  Bone-the-whole. 

I  will  not  give  the  name  of  the  poor  fellow  who  has  fallen  so 

far  below  both  the  honestum  and  the  utile,  to  say  nothing  of  the 

decorum  or  the  dulce.     He  is  the  fourth  who  has  taken  elaborate 

notice  of  me ;  and  my  advice  to  him  would  be,  Nee  quarto,  loqui 

persona  laboret.     According  to  him,  I  scorn  humanity,  scandalize 

learning,  and  disgrace  the  press  ;  it  admits  of  no  manner  of  doubt 

that  my  object  is  to  mislead  the  public  and  silence  truth,  at  the 

expense  of  the  interests  of  science,  the  wealth  of  the  nation,  and 

the  lives  of  my  fellow  men.     The  only  thing  left  to  be  settled  is, 

whether  this  is   due   to   ignorance,  natural   distaste  for    truth, 

personal   malice,  a   wish  to  curry  favour  with  the  Astronomer 

Royal,  or  mere  toadyism.     The  only  accusation  which  has  truth 

in  it  is,  that  I  have  made  myself  a  '  public  scavenger  of  science ' : 

the  assertion,  which  is  the  most  false  of  all  is,  that  the  results  of 

my  broom  and  spade  are  '  shot  right  in  between  the  columns  of ' 

the  Athenaeum.     I  declare  I  never  in  my  life  inserted  a  word 

between  the  columns  of  the  Athenaeum :  I  feel  huffed  and  miffed 

at  the  very  supposition.     I  have  made  myself  a  public  scavenger  ; 

and  why  not  ?     Is  the  mud  never  to  be  collected  into  a  heap  ?     I 

look  down  upon  the  other  scavengers,  of  whom  there  have  been  a 

few — mere  historical  drudges  ;  Montucla,  Hutton,  &c. — as  not  fit 

to  compete  with  me.     I  say  of  them  what  one   crossing-sweeper 

said  of  the  rest :  '  They  are  well  enough   for  the  common  thing  ; 

but  put  them  to  a  bit   of  fancy-work,  such  as  sweeping  round  a 

post,  and  see  what  a  mess  they  make  of  it ! '     Who  can  touch  me 

at  sweeping  round  a  paradoxer  ?     If  I  complete   my  design  of 


ORTHODOX  PARADOX  KS.  401 

publishing  a  separate  work,  an  old  copy  will  be  fished  up  from  a 
stall  two  hundred  years  hence  by  the  coming  man,  and  will  be 
described  in  an  article  which  will  end  by  his  comparing  our 
century  with  his  own,  and  sighing  out  in  the  best  New  Zealand 
pronunciation — 

Dans  ces  terns-la 

C'etait  deja  comme  ca ! 

And  pray,  Sir !  I  have  been  asked  by  more  than  one — do  your 
orthodox  never  fall  into  mistake,  nor  rise  into  absurdity  ?  They 
not  only  do  both,  but  they  admit  it  of  each  other  very  freely ; 
individually,  they  are  convinced  of  sin,  but  not  of  any  particular 
sin.  There  is  not  a  syndoxer  among  them  all  but  draws  his  line 
in  such  a  way  as  to  include  among  paradoxers  a  great  many 
whom  I  should  exclude  altogether  from  this  work.  My  worst 
specimens  are  but  exaggerations  of  what  may  be  found,  occa- 
sionally, in  the  thoughts  of  sagacious  investigators.  At  the  end 
of  the  glorious  dream,  we  learn  that  there  is  a  way  to  Hell  from 
the  gates  of  Heaven,  as  well  as  from  the  City  of  Destruction  : 
and  that  this  is  true  of  other  things  besides  Christian  pilgrimage 
is  affirmed  at  the  end  of  the  Budget  of  Paradoxes.  If  D'Alembert 
had  produced  enough  of  a  quality  to  match  his  celebrated  mistake 
on  the  chance  of  throwing  head  in  two  throws,  he  would  have 
been  in  my  list.  If  Newton  had  produced  enough  to  match  his 
reception  of  the  story  that  Nausicaa,  Homer's  Phaeacian  princess, 
invented  the  celestial  sphere,  followed  by  his  serious  surmise  that 
she  got  it  from  the  Argonauts, — then  Newton  himself  would  have 
had  an  appearance  entered  for  him,  in  spite  of  the  Principia.  In 
illustration,  I  may  cite  a  few  words  from  '  Tristram  Shandy ' : — 

'  "  A  soldier,"  cried  my  uncle  Toby,  interrupting  the  Corporal,  "  is 
no  more  exempt  from  saying  a  foolish  thing,  Trim,  than  a  man  of 
letters." — "But  not  so  often,  an'  please  your  honour,"  replied  the 
Corporal.  My  uncle  Toby  gave  a  nod.' 

I  now  proceed  to  die  out.  Some  prefatory  remarks  will  follow 
in  time.1  I  shall  have  occasion  to  insist  that  all  is  not  barren  : 
I  think  I  shall  find,  on  casting  up,  that  two  out  of  five  of  my 
paradoxers  are  not  to  be  utterly  contemned.  Among  the  better 
lot  will  be  found  all  gradations  of  merit ;  at  the  same  time,  as 
was  remarked  on  quite  a  different  subject,  there  may  be  little  to 
choose  between  the  last  of  the  saved  and  the  first  of  the  lost. 

1  These  remarks  were  never  written. — (Ed.) 


492  A   BUDGET   OF  PARADOXES. 

The  higher  and  better  class  is  worthy  of  blame  ;  the  lower  and 
worse  class  is  worthy  of  praise.  The  higher  men  are  to  be  reproved 
for  not  taking  up  things  in  which  they  could  do  some  good  :  the 
lower  men  are  to  be  commended  for  taking  up  things  in  which 
they  can  do  no  great  harm.  The  circle  problem  is  like  Peter 
Peebles's  lawsuit : — 

'  "  But,  Sir,  I  should  really  spoil  any  cause  thrust  on  me  so  hastily." 
— "  Ye  cannot  spoil  it,  Alan,"  said  my  father,  "  that  is  the  very  cream 
of  the  business,  man, —  .  .  .  the  case  is  come  to  that  pass  that  Stair 
or  Arniston  could  not  mend  it,  and  I  don't  think  even  you,  Alan,  can 
do  it  much  harm."  ' 

I  am  strongly  reminded  of  the  monks  in  the  darker  part 
of  the  Middle  Ages.  To  a  certain  proportion  of  them,  per- 
haps two  out  of  five,  we  are  indebted  for  the  preservation  of 
literature,  and  their  contemporaries  for  good  teaching  and  miti- 
gation of  social  evils.  But  the  remaining  three  were  the  fleas 
and  flies  and  thistles  and  briars  with  whom  the  satirist  lumps 
them,  about  a  century  before  the  Eeformation  : — 

Flen,  flyys,  and  freris,  populum  domini  male  caedunt ; 
Thystlis  and  breris  crescentia  gramina  Isedunt. 
Christe  nolens  guerras  qui  cuncta  pace  tueris, 
Destrue  per  terras  breris,  flen,  flyys,  and  freris. 
Flen,  flyys,  and  freris,  foul  falle  hem  thys  fyffcen  yeris, 
For  non  that  her  is  lovit  flen,  flyys,  ne  freris. 

I  should  not  be  quite  so  savage  with  my  second  class.  Taken 
together,  they  may  be  made  to  give  useful  warning  to  those  who 
are  engaged  in  learning  under  better  auspices  :  aye,  even  useful 
hints  ;  for  bad  things  are  very  often  only  good  things  spoiled  or 
misused.  My  plan  is  that  of  a  predecessor  in  the  time  of  Edward 
the  Second : — 

Meum  est  propositum  gentis  imperitsa 
Artes  frugi  reddere  melioris  vitae. 

To  this  end  I  have  spoken  with  freedom  of  books  as  books,  of 
opinions  as  opinions,  of  ignorance  as  ignorance,  of  presumption  as 
presumption  ;  and  of  writers  as  I  judge  may  be  fairly  inferred 
from  what  they  have  written.  Some — to  whom  I  am  therefore 
under  great  obligation — have  permitted  me  to  enlarge  my  plan 
by  assaults  to  which  I  have  alluded  ;  assaults  which  allow  a  privi- 
lege of  retort,  of  which  I  have  availed  myself ;  assaults  which  give 
my  readers  a  right  of  partnership  in  the  amusement  which  I 
myself  have  received. 


CONCLUSION.  493 

For  the  present  I  cut  and  run  :  a  Catiline,  pursued  by  a  chorus 
of  Ciceros,  with  Quousque  tandem  ?  Quamdiu  nos  ?  Nihil  ne  te  ? 
ending  with,  In  te  conferri  pestem  istam  jam  pridem  oportebat, 
quam  tu  in  nos  omnes  jamdiu  machinaris  !  I  carry  with  me  the 
reflection  that  I  have  furnished  to  those  who  need  it  such  a 
magazine  of  warnings  as  they  will  not  find  elsewhere  ;  a  signatis 
cavetote  :  and  I  throw  back  at  my  pursuers — Valete,  doctores  sine 
doctrina ;  facite  ut  proximo  congressu  vos  salvos  corporibus  et 
sanos  mentibus  videamus.  Here  ends  the  Budget  of  Paradoxes. 


APPENDIX. 


I  THINK  it  right  to  give  the  proof  that  the  ratio  of  the  circumference 
to  the  diameter  is  incommensurable.  This  method  of  proof  was  given 
by  Lambert,  in  the  Berlin  Memoirs  for  1761,  and  has  been  also  given 
in  the  notes  to  Legendre's  Geometry,  and  to  the  English  translation  of 
the  same.  Though  not  elementary  algebra,  it  is  within  the  reach  of 
a  student  of  ordinary  books. 

Let  a  continued  fraction,  such  as 


b  +  c 

d  +  e_ 

7+  &c., 

be  abbreviated  into  ^  each  fraction  being  understood 

b+   d+  f+  &c. : 

as  falling  down  to  the  side  of  the  preceding  sign  + .  In  every  such 
fraction  we  may  suppose  b,  d,  /,  &c.  positive ;  a,  c,  e,  &c.  being  as 
required :  and  all  are  supposed  integers.  If  this  succession  be  con- 

fL        C        P 

tinued  ad  infinitum.  and  if  1,    ^,    -j   &c.   all  lie    between    —    1   and 

oaf 

+  1,  exclusive,  the  limit  of  the  fraction  must  be  incommensurable 
with  unity ;  that  is,  cannot  be  -  ,  where  A  and  B  are  integers. 

First,  whatever  this  limit  may  be,  it  lies  between  —  1  and  +  1. 

This  is  obviously  the  case  with  any  fraction  -t- ,  where  w  is  between 

q  +   w 

+  1  :    for,  -?,  being   <  1,  andp  and  q  integer,  cannot  be  brought  up 

2 
to  + ,   by  the  value  of  w.     Hence,  if  we  take  any  of  the  fractions 

a     a       c     a       c        e      » 
6     6+    d'    6+    d  +   f  ' 

say   -  •?  we  have,  -2-  being  between  +  1,  so  is  -  .     so 

J    b+    d r   /+    &  h  f+     h 

therefore  is  f        —      —  ;  and  so  therefore  is  -^      — ' 

d+   /+   k  64   rff    /+    // 


496  APPENDIX. 

e,   e 
integers.     Let 

P  =  A  'I-          '       &C,     Q  =  P   *-       f       &C.,    R  =  Q  !         i        &C. 


Now,  if  possible,  let  —  &c.  be    -    at  tlie  limit  ;  A  and  B  being 

o+    d+  B 


p,  Q,  K,  &c.  being  integer  or  fractional,  as  may  be.     It  is  easily  shown 
that  all  must  be  integer  :  for 

or,  P  =  a  B  —  I  A 


B          6   +  P 

A' 

p  /> 

-  =   , or,  Q  =  c  A  —  d  p 

A         d  -t-   Q 

p 
Q  _  e 


/  + 


or,  R  =  e  P  —  /  Q 


&c.,  &c.     Now,  since  a,  B,  6,  A,  are  integers,  so  also  is  P  ;  and  thence 

Q  ;  and  thence  K,  &c.     But  since-,    -,    ~,    -,  &c.  are  all  between  —  1 

B     A     P     Q 

and  +  1,  it  follows  that  the  unlimited  succession  of  integers  P,  Q,  K, 
are  each  less  in  numerical  value  than  the  preceding,  Now  there  can 
fee  no  such  unlimited  succession  of  descending  integers  :  consequently, 

it  is  impossible  that    -         —      &c.  can  have  a  commensurable  limit. 
6+     dx 

It  easily  follows  that  the  continued  fraction  is  incommensurable  if 
--,    -,    &c.,  being  at  first  greater  than  unity  become  and  continue  less 

than  unity  after  some  one   point.     Say  that    -,    —  ,  .  .  .    are  all   less 

K     m 

than  unity.     Then  the  fraction  —       —       ...   is  incommensurable,  as 

k+    m  + 

proved  :  let  it  be  K.     Then  £  -  is  incommensurable,  say  X  ; 


, 
h  +  K  /  +  A 

is  the  same,  say  p  ;  also    c-  -  ,  say  r,  and  —  -  ,  say  p.     But  p  is 

d  +  /i  o  +  v 

the  fraction  -  —  -  —  .  .  .  itself  ;  which  is  therefore  incommensurable. 
6+  d  + 

Let  (j)  z  represent 

1   +  °L  +  a*  +  «3  . 

z       2z  (z  +  1)    r  2-3-  z  0  +  1)  0  +2) 

Let  z  be  positive  :  this  series  is  convergent  for  all  values  of  a,  and 


APPENDIX.  497 

approaches  without  limit  to  unity  as  z  increases  without  limit.  Change 
z  into  z  +  1,  and  form  0  z  —  $  (z  +  1)  :  the  following  equation  will 
result 


or  a  = 


Z  <I>   Z  Z  (ft  Z  Z   +    1    0    (2    +    1) 

(\ 
z   +    \{/  (z  +  1)  I 
/ 

»//  z  being  --  ?-i '-  ;  of  which  observe  that  it  diminishes  without 

z          <t>  z 

limit  as  z  increases  without  limit.     Accordingly,  we  have 


a          i  /     ,    o\    » 
(z  +  3),  &c. 


2+  (z  +  1)+  (z  +2) 

And,  x//  (z  +  n)  diminishing  without  limit,  we  have 

a    4  (a  -f  1)  _      a  a  a  a 

?>»          "  2  +  (2  +  1)  +   («>  2)~+   («~+  3)  +  ... 

Let  z  —  \;   and  let  4  a  =  —  a2.      Then  -     0  (z  +  1)  is  —      > 


2  '  2 

or  cos  x  :  and  the  continued  fraction  is 


a; 
_    op  —  _  _ 

f  +  ...  21+3+ 

2 


25          «•«    35*     ^—    r?j*     ^^    33 

whence  tan  x  = 


1+3+      5+      7+  ... 


Or,  as  written  in  the  usual  way, 
tan  x  =  x 


1  2 

3^^  a;2 

5  -a;2 


7-  ... 

K  K 


498  A   BUDGET   OF  PARADOXES. 

This  result  may  be  proved  in  various  ways  :  it  raay  also  be  verified 
by  calculation.     To  do  this,  remember  that  if 


Pj    =  CSj    P2  =  &2  Pl»  P3==^3   P2~^~tt3  PH    P4  =  ^4  P3  ~$~  a4   P2)   "^C- 

in  the  case  before  us  we  have 

a    —.  rjl,  a    — .  yfi   a    =  x?  a    :=  x^  a    =  a;2   &c 

Z>,  =  1,  &2  =  3,         63  =  5,         &4  =  7,        &5  =  9,  &c. 

PI  =  x  QJ  =  1 

P3  =  15  x  —  x3  Q3  =  15  —  6  a;2 

P4  =  105  x  -  10  x3  Q4  =  105  -  45  a;2  +  x* 

p5  =  945  x  -  105  x3  +  x5  Q5  =  945  -  420  a-2  +  15  a;4 

P6  =  10395  x  -  1260  xs  +  21aj5  Q6  =  10395  -  4725  a;2  +  210  x4  -  XG 

We  can  use  this  algebraically,  or  arithmetically.  If  we  divide  pn  by 
Qn,  we  shall  find  a  series  agreeing  with  the  known  series  for  tan  x,  as 
far  as  n  terms.  That  series  is 

«3        2  x5        17  x7        62  x9 
*"  3        Id~       315          2835  " 

Take  P5,  and  divide  it  by  Q5  in  the  common  way,  and  the  first  five 
terms  will  be  as  here  written.  Now  take  x  =  '1,  which  means  that 
the  angle  is  to  be  one  tenth  of  the  actual  unit,  or,  in  degrees  5°'  7295 78. 
We  find  that  when  x  =  '1,  P6  =  1038-24021,  Q6  =  10347-770999 ; 
whence  PG  divided  by  Q6  gives  '1003346711.  Now  5°'729578  is  5°  43' 
46J" ;  and  from  the  old  tables  of  Rheticus — no  modern  tables  carry 
the  tangents  so  far — the  tangent  of  this  angle  is  '1003347670. 

Now  let  x  =  ^  TT  ;  in  which  case  tan  x  =  1.  If  £  TT  be  commensur- 
able with  the  unit,  let  it  be  —,-m  and  n  being  integers  :  we  know  that 
^  TT  <  1.  We  have  then 

1  = 


m 


n        n2       w2  n  —  3  n  —  5  n  —  7  n  —  ... 


o  O  n 


Now  it  is  clear  that  -  —  ,    --  —  ,    -  -  —  ,  &c.  must  at  last  become  and  con- 

3  n     b  n     7  n 

tinue  severally  less  than  unity.     The  continued  fraction  is  therefore 
incommensurable,  and  cannot  be  unity.     Consequently  ?r2  cannot  be 


APPENDIX.  499 

commensurable  :  that  is,  TT  is  an   incommensurable  quantity,  and  so 
also  is  7T2. 


I  thought  I  should  end  with  a  grave  bit  of  appendix,  deeply  mathe- 
matical :  but  paradox  follows  me  wherever  I  go.  The  foregoing  is — in 
my  own  language — from  Dr.  (now  Sir  David)  Brewster's  English 
edition  of  Legendre's  Geometry,  (Edinburgh,  1824,  8vo.)  translated 
by  some  one  who  is  not  named.  I  picked  up  a  notion,  which  others 
had  at  Cambridge  in  1825,  that  the  translator  was  the  late  Mr. 
Galbraith,  then  known  at  Edinburgh  as  a  writer  and  teacher.  But 
it  turns  out  that  it  was  by  a  very  different  person,  and  one  destined 
to  shine  in  quite  another  walk  ;  it  was  a  young  man  named  Thomas 
Carlyle.  He  prefixed,  from  his  own  pen,  a  thoughtful  and  ingenious 
essay  on  Proportion,  as  good  a  substitute  for  the  fifth  Book  of  Euclid 
as  could  have  been  given  in  the  space ;  and  quite  enough  to  show  that 
he  would  have  been  a  distinguished  teacher  and  thinker  on  first 
principles.  But  he  left  the  field  immediately. 


(The  following  is  the  passage  referred  to  at  p.  285  : — Ed.) 

Michael  Stifelius  edited,  in  1554,  a  second  edition  of  the  Algebra 
(Die  CW.),  of  Christopher  Rudolf.  This  is  one  of  the  earliest  works 
in  which  .+  and  —  are  used. 

Stifelius  was  a  queer  man.  He  has  introduced  into  this  very  work 
of  Rudolph  his  own  interpretation  of  the  number  of  the  Beast.  He 
determined  to  fix  the  character  of  Pope  Leo  :  so  he  picked  the  numeral 
letters  from  LEODECIMVS,  and  by  taking  in  x  from  LEO  x.  and  striking 
out  M  as  standing  for  mysterium,  he  hit  the  number  exactly.  This 
discovery  completed  his  conversion  to  Luther,  and  his  determination 
to  throw  off  his  monastic  vows.  Luther  dealt  with  him  as  straight- 
forwardly as  with  Melancthon  about  his  astrology:  he  accepted  the 
conclusions,  but  told  him  to  clear  his  mind  of  all  the  premises  about 
the  Beast.  Stifelius  did  not  take  the  advice,  and  proceeded  to  settle 
the  end  of  the  world  out  of  the  prophet  Daniel :  he  fixed  on  October, 
1533.  The  parishioners  of  .some  cure  which  he  held,  having  full  faith, 
began  to  spend  their  savings  in  all  kinds  of  good  eating  and  drinking ; 
we  may  charitably  hope  this  was  not  the  way  of  preparing  for  the 
event  which  their  pastor  pointed  out.  They  succeeded  in  making 
themselves  as  fit  for  Heaven  as  Lazarus,  so  far  as  beggary  went :  but 
when  the  time  came,  and  the  world  lasted  on,  they  wanted  to  kill 
their  deceiver,  and  would  have  done  so  but  for  the  interference  of 
Luther. 


INDEX. 


(A.  C.)  Auti-Copernican,  (Ale.)  Alchemist,  (A.  N.)  Anti-Newtonian,  (Ast.)  Astrologer, 
(Cyc.)  Cyclometer,  (Mys.)  Mystic,  (Tris.)  Trisector. 


ABB 

ABBOTT,  Chief  Justice,  108 
—  On  Hone's  trial,  108 
Aboriginal  Britons  (Poem),  432 
Academy  of  Sciences,  French,  97 
Adair,  Serjeant,  133 
Adam,  Melchior,  44 
Adams,  J.  C.,  discoverer  of  Neptune,  31.53, 

211,  253,  337,  343,  344,  347,  348,  451 
Addison,  Joseph,  111 
Ady,  Joseph  (begging  letter  writer),  276, 

277 

Agnew,  H.  C.  (Pyramid  Quadrature),  199 
Agricultural  Labourer  (letter  of),  259 
Agrippa,  Cornelius,  33,  34 

—  King,  147 
Ainsworth,  Harrison,  337 

Airy,  G.  B.,  54,  55,  56,  343,  350,  362,  480 

—  Mrs.,  143 
Albert,  Prince,  286 
Aldrovand,  Father,  332 
Alfonso  X.,  of  Castile,  431 
Alford,  Dean,  398 

Alfred,  King,  (ballad  of),  263 
Aloysius  Lilius  (Calendar),  222 
Ameon  Uey,  258 

Amicable  Society  (Constitution  of),  212 
Amphisbcena  Serpent,  23;  Sir  T.  Browne's 

remarks  on,  23 

Anagrams  on  Author's  name,  82,  83 
Anaxagoras,  288 
Anghera,  Dr.  (Cyc.),  289 
Anopides  of  Chios,  288 
Antegregorian  Calendar,  225 
Antinomians,  The,  244 
Antipho,  (Cyc.),  288 
Antiquary,  The.  34 
Antonie,  Dr.  Francis,  75 
Apocalypse,  The,  398,  399,  400 
Apollonius,  30,  53,  71 
Apparitions,  280 


ADZ 

Arago,  M.,  144,  176,  198,  241,  242 

Aratus,  361,  362 

Arbuthuot  (to  Swift),  79 

Archer,  Henry,  (Zetetic  Astronomer,)  308 

Archimedes,  4,  8,  30,  31,  53,  68,  303,  389, 

392,  470 

Argoli,  Andrew  (Ast.,)  65 
Ariosto,  78 
Aristotle,  4,  28,  30,  49,  51,  56, 144,  200, 

201,  202,  203,  204,  209,  288,  384,  385, 

387,  490 

Aristophanes,  356,  436 
Arithmetical  Books,  De   Morgan's,    136, 

454 

Arnobius,  297 

Arson,  P.  J  ,  (Calendrier  Universel,)  388 
Articles  (Thirty-nine),  427 
Articles  of  War,  249 
Assurance  Magazine,  69 
Astrology,  277,  278,  279 
Astronomer  Royal,  320,   313,   445,  451, 

460,  479,  480,  481 

Astronomer's  Drinking  Song,  234,  235 
Astronomical  Committee,  370 
-  Police  Report,  241,  242.  •_'  1:1 

—  Society,  19.  20,  21,  178,  194,  230,  231, 
232,  233,  307,  347,  350,  370,  449,  479, 
480 

Astunica,  Didacas,  57 
Athanasian  Christianity,  84 

—  Creed,  107,  199,  200,  228,  271,  273 

—  Doctrine,  3 

Athenamm,  The,  5,  194,  205,  216,  236, 
239,  243,  256,  284,  311,318,  324,  325, 
333,  338,  387,  399,  408,  409,  421,423, 
459,  470,  475,  477,  490 

—  Review  of  James  Smith,  321,  et  scq. 
Augustine,  St.,  263 

Austin,  Jane,  114,  154 

Auzout  (Macclc«field  Letters),  451 


502 


INDEX. 


BAB 

•pABBAGE,  Charles,  123,  175,  370 
_D     Bacon,  Francis,  4,  48,  49,  50,  51,  52, 
53,  54,  55,  56,  57,  84,  85,  86,  87,  200, 
467,  468,  469 

Bacon,  Roger,  4,  75,  221,  310 
Bailly,  99,  165,  186 
Baily,  Francis,  186,  187,  258,  374 
—  Richard,  (Hussein  Effendi),  258 
Baker,    Thomas   (Macclesfield    Letters), 

451,  453 

Bakewell  (A.  N.),  354 
Bale,  25 

Banks,  Sir  Joseph,  20 
Barker's  Bible  (Inscription  in),  428 
Barker,  Mr.  (Hutchinsonian),  140 
Baronius,  24,  25,  26,  27,  290 
Barrett's  Method  (Review  of),  374 
Barrow,  Isaac,  123,  451 
Basanistes,  141 
Bassano,  Due  de,  250,  474 
Bayle,  297 
Baveme,  30 

Baxter,  Thomas  (Cyc.),  87 
Beaufort,  Admiral  Sir  Francis,  429 
Beaugrand  de  (Cyc.),  72,  73 
Beaulieu,  Pontault  de,  71 
Becourt,    de   (Hindu   Philosophy),   436, 

437 

Belimen,  Jacob,  (Mys.),  100,   151,    460, 
461,  462,  463,  464 

Bentley,  Richard,  67 

Bernard  (Macclesfield  Letters),  449 

Bernouilli,  James,  204 

—  John,  89,  204 

Bertit  (Macclesfield  Letters),  450 

Bessel,  250 

Bethune,  Drinkwater,  62,  167,  174 

Beza,  44 

Bible,  The,  Authorised  Version,  467 

Bickersteth,  Rev.  E.  H.  141,  142 

Biddle,  John,  141 

Biden,  James  (Prophet),  357,  358 

Biot,  54,  56 

Birch  (Hist,  Royal  Society),  66,  451,  456, 
457 

Birks,  T.  K.  (On  Matter  and  Ether),  355 

Bishop,  George  (Observatory),  238 

Blast,  Dr.  (Antinomians),  244 

Blunt,  Gregory,  141 

Board  of  Longitude,  97 

Boccaccio,  41 

Boethius,  31 

Boetius,  31 

Bonaventura  Piscator,  265,  268 

Boncompagni,  Prince  Balthasar,  179 

Boniface,  Archbishop,  24,  25,  26 

Boole,  George,  154,  155,  201,  297,  et  scq. 

Borelli  (Macclesfield  Letters),  450 

Borello,  Pellegrino  (Cyc.),  46 

Borron,  Mrs.  (on  Neptune),  253 

Bosanquet,  Lieut.,  282 

Boscovich,  93,  98 


CAM 

Bouguer  (Macclesfield  Letters),  451 
Bouillaud,  82,  448 
Bouvard,  M.,  198 

—  Report,  176 

Bovillus,  Charles  (Cyc.\  31,  32,  465 
Bowring,  Sir  J.,  216,  422 
Boyle,  Robt.,  21,  75,  78,  450 
Bradwardine  (Cyc.),  136 
Brahe,  Tycho,  49,  72 
Brancker,  450 

Brandon,  Jacob,  (Tobacconist,)  283 
Brennan,  Justin,  200 
Brewster,  Sir  David,  81,  83,  87,  393,  499 
Briggs,  46,  450,  451 
Bright,  John,  408 
Bryso,  288 

British  Association,  The,  256,  318,  372, 
478,  483 

—  in  jeopardy,  408 

• —  James  Smith's  letter  to,  316 

Brothers,  Richard,  (Mys.)  190,  191,  313 

Brougham,  Lord,  146,  153,  178 

Brouncker,  Lord,  78,  451 

Browne,  Sir  Thomas,  23 

Briicker,  41 

Briinnow,  Dr.  (on  Neptune)  238,  241 

Bruno,  Giordano,  41 

Buffon,  170 

Bungus,   Peter  (Mystical  Numbers),  37, 

38,  39 

Bunyan,  John,  44,  87,  113 
Buonaparte,  Napoleon,  137,  145,  190 
Burial  Service,  The,  264,  265 
Buridan,  28,  29 
Brunei,  249 
Burnet,  66,  69 

Burney,  Fanny,  113,  114 

Busby,  Dr.,  (Westminster  School,)  457 

Burton,  Frances  Barbara,  230 

Buteo,  35 

Byrgius,  Justus,  35 

Byrne,  Oliver,  200,  373,  374,  375,  376 

Byron,  Lady  Noel,  435 

Byron,  Lord,  111,  431,  et  scq. 


pABBALA    ALGEBRAICA,     162,    et 

\J         seq. 

Cabbala  Alphabetica,  1 63,  et  seq. 

Cabinet  Cyclopaedia,  The.  420 

Caleb  Quotem,  246 

Calender,  Harry  (Wit),  283 

Calendar,  Ecclesiastical,  219,  et  scq. 

—  Gregorian,  219,  et  seq. 

—  Jewish,  219,  et  seq. 

—  Julian,  219,  et  seq. 

Cambridge,  Defective  teaching  at,  420, 
421 

—  Disputations,  305 

-  Phil.  Trans.,  281,  329,  375 
Canipanus  (Cyc.),  31 


INDEX. 


503 


CAN 

Canning,  George,  346 

Cantab  (Letter  of  a),  333 

Carcavi,  65 

Cardanus,  287 

Carlyle,  Thomas,  499 

Casaubon,  Isaac,  67 

Case,  John  (Ast.),  76 

Cassini,  James,  102,  103,  278 

Castel,  Father,  (A.N.)  88 

Castiglione,  83 

Castle    of  Knowledge   (dialogue   from), 

467 

Castlereagh,  Viscount,  111 
Catcott,  Dr.,  140 
Cataldis  (Cyc.),  46 
Catiline,  493 
Cavalieri,  65 
Cavendish,  Charles,  65,    174,    175,   450, 

457 

Cayley,  George,  446 
Celtic  Druids,  The,  166 
Centrifugal  Force,  431 
Challis,  Professor,  239,  240,  242,  343 
Chalmers,  Rev.  Dr.  (666),  397 
Chambers's  Dictionary,  439 
Charles  II.  King,  19,  282 
Charlemagne,  77 
Charles  IX.  (of  France),  310 
Charles  X.  (of  France),  250 
Chasles,  M.,  29 
Chaucer's  Rhymes,  469 
Chemistry  (or  Chymistry),  75 
Chehterfield,  Lord,  450 
Childhood  and  Priesthood,  401 
Chitty  (or  Kitty),  464 
Christian  Observer,  The,  217 
Christian  (The  name),  146,  147,  148 
—  (The  word),  263 
--(Roman),  266,  267,  268 
Christianity  and  war,  249 
Church,  The,  270,  271,  272,  273,  274 
Church  of  England  and  Ireland,  The,  269 
Church  Times,  The,  309 
Cicero,  493 

Circulation  of  the  Blood,  254 
Ciruelo,  Petro  Sanchez  (Ed.  of  Bradwar- 

dire),  136 

Clairault,  Alexis  Claude,  131,  132,  236 
Clarke,  Richard  (Mys.),  151 
Clavius,  Christopher,  9,  26,  46,  67,  68, 

217,  cfseq.,  287 
Cluvier,  Dethleu  (Cyc.),  470 
Cluvier,  Philip,  470 
Cobbett,  William,  105,  119,  120,  122 
Cocker's  Arithmetic,  30,  291,  454,  45-5 
Cody,  Patrick,  (Tris.)  389 
Coincidences,  279.  et  scq. 
Coke,  Chief  Justice,  469 
Colbinus,  Father  Philip,  44 
Colburn,  /oral),  ;V> 
Colenso,  Bishop,  52,  146 
Collectanea  Chymica,  7-"> 


DEC 

Collins,  John,  6,  66,  449,  et  scq. 

Columbus,  Chr.,  81 

Colvill,  William  Henry,  293 

Comets  as  Volcanoes,  303 

Cometic  Astrology,  76 

Cominale,  Celestiuo,  96 

Commercium  Epistolicum,  449 

Companion  to  the  Almanac,  The,  217 

Comptes  Rendus.  54 

Conduitt,  Mrs.,  81 

Congregation  of  the  Index,  57 

Convocation,  228 

Convocation  of  Oxford,  60,  61 

Cook,  Chief  Justice,  469 

Copernicus,  2,  4,  5,   49,   57,  58,   59,  60, 

61,  72,  81,  151,  161,  301,  360,  361 
Cooper,  Thomson,  174 
Cormouls,  Thomas,  134 
Correspondent,  The,  408,  409,  472,  4?8, 

479,  481 

Cosmo  de'  Medici,  448 
Cotes,  451 

Cottle  Church,  The,  313,  et  seq.,  358 
Council  of  Nicaea,  220 

—  Trent,  222 

Counter  Doggrel.  Logical,  208,  209 
Craig,   John     (Mathematical   Theology), 

77,78 

Cribb,  Tom,  190 
Cromwell,  Oliver,  470 
Crossley,  Mr.,  232 
Cruickshank,  George,  111 
Cumberland,  Duke  of,  120 
Cumyns,  Eliza,  180 
Cunuiugham,  John  (A.C.),  103 
Cusa,  Nicolaus  de  (Cyc.),  33,  221 
Cyclometer's  Letters,  259,  260 
Cyclometry,  (James  Smith),  316,  et  seq. 

—  Remarks  on,  389,  et  seq. 

—  Versified  (Valentinus),  36 
Cyclopaedia  of  Physical  Science,  444 
Cyropaedia,  439 


DAEDALUS   BR1TANNICUS  (Flying 
machine),  253 
D'Alembert,  236,  440,  491 
Dalgarno,  70 
Dalmas,  A.,  436 
Dante,  297,  436 

Darwin  (Botanic  Garden),  253,  254 
Dary,  Michael,  452,  453 
Dary's  Problem,  456 
Davies,  Thomas  Stephens,  350,  351,  374 
Day,  Dr.  Alfred,  177,  178 
Dean,  William  (Cyc.),  458 
DeBeaume,  288 
Debenham,    Commander,   R.N.,  (Tides), 

243 

De  Castres,  Sabatier,  429 
Dechales,  32 
Decimal  Coinage,  363,  364,  365,  366 


504 


INDEX. 


DEO 

Decimal  System,  The,  301 
Declaration  of  Belief,  421,  et  seq. 

—  (Proposed  substitute),  423,  424,  425 
De  Causans,  179 

Dee,  John  (Ast.),  451 

De  Faure  (Gyc.),  89,  410 

De  la  Leu  (Cyc.),  179 

Delambre,  62,  99,  217,  360 

De  Moivre,  18,  99,  232,  4';0 

De  Molina,  Alphonso,  179 

Demonville,  175,  176 

De  Morgan,  Arithmetical  Books,  136,  454 

—  Captain,  282 

—  Baron,  352 

—  Professor,  in  the  Pillory,  409 

—  and  Macaulay,  465 
Dennison,  Joseph,  213,  216 
D6saguliers,  93 
Desargues,  72 

Descartes,  4,  40.  65,  98, 122, 123,  235,  310 

De  Sepres,  P.  Y.,  167 

De  Serres,  Olivier,  288 

De  Thou,  35,  67,  68,  448 

De  Vausenville,  9 

D'ckens,  Charles,  483 

Diderot  (confuted  by   Euler),    250,   251, 

474 

Digby,  Kenelme,  16,  66 
Digges,  Thomas,  451 
Dircks,  Henry,  342 
Discoveries  and  Discoverers,  387 
D'Israeli,  Isaac,  69,  70,  71,  81,  112,  135 
Ditton,  Humphry,  79 
Diocletian,  221 
Dionysius  Exiguus,  221,  222 
Divine  Mystery  of  Life,  341 
Dobson,  J.,  (The  Unpunctuating),  1 39, 140 
Dodson,  John,  457,  458 
Dollond,  232 
Double  Vahu,  395,  et  seq. 
Drach,  Solomon,  460 
Drayson,  Captain,  338,  339 
Dryden,  Religio  Laici,  295 
—  The  Hind  and  Panther,  401 
Dual  Arithmetic  (Oliver  Byrne),  373 
Dublin  Review,  The.  267 
Duchesne,  Van  der  Eyck  (Cyc.),  35,  36,  62 
Duelling,  248,  249 
Du  Fan,  189 

Duke,  Sir  James  (Lord  Mayor),  277 
Dumortier,  189 
Dunbar,  John  (Cyc.),  179 
Dunciad,  The,  436 
Dunkin,  Mr.  E.,  480 
Dupuis,  Peter,  448 
Dutens,  (Ed.  of  Leibnitz,)  308 
Dyer,  George,  106 


TOASTER-DAY,  217,  et  seq. 
Jj     East  India  Company,  231 
Ecclesiastical  Society,  219 


FOS 

Sdgewortli,  Maria,  114 
Edinburgh  Review,  193,  435 
Editorial  Duties  (Letter  on),  11,  et  seq. 
"dleston,  Mr.,  449 
IdwardIL,  492 
Edwards,  Dr.  John,  86 

—  Thomas,  68 
:KK\ij(ria,  269,  270 
Elective  Polarity,  230 
Elephant,  (Anecdote  of,)  39,  40 
Elizabeth,  Queen,  76 
Ellenborough,  Lord,  108,  109 
Ellis,  Robert  Leslie,  49,  et  seq. 
B.  M.  to  James  Smith,  319,  331 
Encyclopaedia  Britannica,  438,  443 

—  Metropolitana,  441,  et  seq. 

—  Scientiarum  Omnium,  439 
Encyclopedic,  L',  440 

English  Cyclopaedia  (Art.  on  Quadrature), 
290,  291 

—  60,  61,  62,  293,  438,  et  seq. 
English  Leader,  248 
Epacts,  Table  of,  228 

Epistolae  Obscurorum  Virorum,  193 
Epps,  Mr.  (See  Ast.  Soc.),  91 
Erasmus,  67 
Erastus,  Thomas,  44 
Ericksen,  Niels  (Cyc.),  97,  98 
Ersch  and  Gruber  (Cyclopaedia),  440 
Erskine,  Lord,  334 
Evangelicism,  43 
Evelyn,  John,  66 

TMIRPLAY'S  Letter,  472 

JL      Fancourt,  Samuel,  291 

Faraday,  Michael,  482 

Ferguson,  James,  261,  262 

Fermat,  451 

Ferrari,    'Baron    (Duodecimal    System), 

293,  371 
Fielding,  113 

Fielding's  Miscellanies,  435 
Fienus,  Thomas,  48 
Fifteens  of  Bungus,  38,  39 

—  The  Royal  Society,  38,  39 
Filopanti,  310 
Finleyson,  Thomas,  190 
Finsecus,  Orontius,  (Cyc.),  35,  68 
Flamsteed,  John,  56,  187,  278,  279,  283, 

451,  452,  453,  454 

—  Margaret  (Valentine),  188 
Fletcher,  Captain  J.,  282 

—  Mr.,  (Mathematical  Society,)  233 
Fludd,  Robert,  461 

Folkes,  Martin,  16,  81 

Fontenelle,  81,  121 

Forbes,  President,  140 

Formal  Logic,  94,  201,  et  srq.,  297,  298 

Fomian,  Captain  (A.N.),  178,  185, 

Forster,  Thomas  Ignace  Maria,  194,  195 

Foscarini,  67 

Foster,  (Lect.  Gresham  College,)  456 


INDEX. 


505 


FOU 

Fourrier,  292 

Fox,  George,  245,  246 

Francis,  Philip,  312 

Francceur,  L.  B.,  284 

Franklin,  Benjamin,  429 

Free  Press.  The,  342 

Freher,  Andreas  (Mys.),  461 

French  Lottery,  168,  169 

Freud,  William,  117,  118,  119,  123,  124, 

149,  186 

Fresnel,  280,  281 
From  Matter  to  Spirit,  Reviews  of,  378  to 

388 

Fromondus,  Libertus,  48,  62 
Frost,  Isaac  (Muggletonian),  244,  215 
Fry,  Elizabeth,  133,  134 
Fulton  (Engineer),  88 


ft  ADBURY,  John  (Ast.),  69 

Vj     Galbraith,  Mr.,  499 

Galileo,  4,  5,  24,  26,  40,  49,  53,  60,  61, 

81,  134,  144,  235,  320,  383,  430 
Galloway,  Thomas  (Fifteens),  39 
/        —  and  James  Ivory,  345 

Garrick,  David  (couplet),  16 

Gascoigne  (Macclesfield  Letters),  450 

Gassendi,  66 

Gauss,  187 

Geber  (Arabian),  288 

Gentleman's  Magazine,  The,  151,  282 

General  Dictionary,  The,  451 

Geological  Society,  The,  21 

Gergonne,  204 

Ghetaldus,  53 

Gibbon,  Edward,  154 

Gilbert,  William,  5,  45,  49 

Gillott's  Steel  Pens,  459 

Gladstone,    William    Ewart,    353,    407, 

417 
Godwin,  Bishop,  135 

Golius,  65 

Gompertz,  Benjamin,  233,  236 

Gonsales,  Domingo,  135 

Goulburn,  Hon.  H.,  173,  174,  175 

Goulden,   S.   (Zetetic   Astronomy),    306, 
307,  308 

Grandamicus,  Jacobus,  65 

Grange,  Armand  (Cyc.),  316 

Grant,  Professor  (Hist.  Astronomy).  243, 
337 

Grassini,  Signora,  137 

Graunt,  John,  68,  69 

Gray's  Bard,  434 

Greene,  Robert,  80,  81 

Gregg,  Tresham  Dames,  297,  et  srq. 

Gregorian  Calendar,  The,  217,  et  scq. 

Gregory,  David,  44,  451 

—  James,  71,  123,  124 

—  Olinthus,  295 

—  Pope,  222,  223,  224 
(hvvil,  Sir  Fulk.  120 


HOB 

Grey,  Earl,  191,  416 

Grosart,  Alexander,  84,  85,  86,  87 

Grove,  Edward  (Correlation  of  Force),  462 

Gruenberger,  Christopher,  46 

Grynseus,  Thomas,  44 

Guldinus,  53 

Gunning  (Reminiscences  of  Cambridge), 

118,  154 
Guthrie  (Astronomy),  244 


HAILES,  J.   D.,  Challenge  to  Astrono- 
mical Society,  339,  340 
Hale,  Matthew,  73,  74 

—  Sir  William,  74 
Hales,  Stephen,  74 
Hall,  Basil,  3/0 

Hallam,  Henry,  56,  95,  434,  464,  467 

Halley,  123,  451,  470 

Halliwell,  John  Orchard,  349,  350,  351, 

449 
Hamilton,  Sir  William,  68,  70,  201,  ct  arq., 

284 

—  Sir  W.  Rowan,  22,  201,  317,  324,  325, 
422,  476 

Hampden,  John,  206 

Hardy,  Matthew,  179 

Hardy,  Thomas,  106 

Harriot,  451 

Harmonicon  Coeleste,  448 

Hatto,  Bishop,  473 

Hauff,  136 

Hawksbee,  93 

Hawkins,  John,  454 

Hawthorne,  Nathaniel,  281 

Headlong  Hall,  475 

Heath,  Douglas  D.,  49 

Heinfetter,  Herman,  311 

Herbart,  J.  F.,  150 

Herigenius,  288 

Herschel,  Sir  John,    52,   178,    179,  180, 

181,  185,  197,  237,  238,  239.  242.  307, 

311,  370,  421,  422,  426 
Herschel,  Sir  William.  52,  90,   134,  135, 

138,  180,  192,  480 
Heteropath's  Letter,  159,  160,  161 
Heywood  (Analysis  of  Kant),  282 
Hicks,  J.  Power,  (Computation,)  292 
Higgins,  Godfrey,  152 
-  Celtic  Druids,  164,  165,  166, 
Hilary,  Pope,  221 
Hill,  Sir  John,  16,  17,  18 

—  Rev.  Rowland,  114 

—  Sir  Rowland,  98,  137 
Hind,  William,  238 
Hippocrates,  287 

Historical  Society  of  Science,  4  !9 

Hoar,   Mr.,    Master   of  the   Mint,    4."6, 

457 
Hobbes,    Thomas,   65,    66,    67,    85,    81, 

301 
Hobhoxis",  John  Cam,  334 


506 


INDEX. 


HOD 


LIB 


Hodder's  Arithmetic,  429 
Hodges,  Walter,  140 
Hodge,  0.  B.,  69 
Hoffman,  136 
Holloway,  Dr.,  140 

Holyoake,  G.  J.  (TheReasoner),  247,  248 
Hone,  William,  74,  106,  et  seq. 
Hooke,  49,  450 
Hook,  Theodore,  425 
Hopkins,  James  (Sun  Paradox),  276 
Horace  (Sham),  475 
Home,  Bishop,  90,  91,  93,  140 
—  George,  92 
Horner,  Leonard,  105 
Homer's  Method,  292,  374,  375 
Horner' s  Papers,  351 
Houlston.  William  (Cyc.),  354 
Howard,  Edward,  78,  79 
Howitt,  William  (History  of  the  Super- 
natural), 378 
Howison,  William,  151 
Howley,  Archbishop,  43 
Hudibras  (Quotation  from),  396 
Hulls,  Jonathan,  88,  254 
Hume,  Joseph,  216 
Hussein  Effendi,  258 
Huyghens,  62,  64,  71,  123,  140,  450,  454 


TNDEX  EXPURGATOIIIUS,  265 

_L     Inglis,  John  Bellenden,  283 

Innocent  I.,  Pope,  220 

Irving,  Rev.  Ed.,  284 

Ivory,  James,  345,  346 

Interminable  fraction  II,  171, 172,  413 


TACK,  Richard,  88 


Jacobitism,  43 
Jacotot,  167 
Jacquard,  27 

Jameson,  Anna  (Legendary  Art),  9.90 
Janson  (Cyc.),  179 
Jeffries,  Judge,  109 
Jenner,  Dr.  (Vaccination),  386 
Jewish  Passover,  217 
Johnson,  Samuel,  15,  266,  417,  433,  447 
• — •  Henry  Coleman  (Cyc.,  &c.),  214 
Johnston,  W.  Harris,  292 
John  the  Baptist,  43 
Jonchere,  M.  de  la  (A.N.),  87 
Jones,  Rev.  W.  (of  Nayland),  140,  et  seq. 
—  William,  449,  et  seq. 
Jonson,  Ben,  10 
Jokeby,  470 

Jopling  (Great  Pyramid),  312 
Journal  of  Education,  173 
Julian  Calendar,  221,  et  seq. 
Junius's  Letters  (Author  of),  313 


KANT  Immanuel,  153,  154,  282 
Kater,  Captain,  8 
Karsten  (parallels),  136 
Kastner,   31,  67,  68 
Keckermann,  Claudius,  3 
Keill  (Macclesfield  Letters),  251 
Kepler,  49,   53,   55,  80,  213,   235,   360, 

361 

Kerrigan,  Lieut.,  186,  216 
King,  Dr.,  146 
Kircher  (Adolphe),  64,  136 
Kirkringius,  74 
Kittle,  Samuel,  140 
Knight,  Charles,  321,  444 

—  Go  wan,  93 

—  Payne,  434 

Kcenig,  S.  (Attestation  of  De  Faure),  89 


T  ACOMME,  Joseph  (Cyc.),  32,  33,  322 

Ji.J  La  Condamine  (Macclesfield  Let- 
ters), 451 

Lacroix,  (Ed.  of  Montucla's  History  of 
Cyclometry),  95,  289 

Lactantius,  25,  58,  60 

Lagrange,  173,  189,  250,  305 

Laing,  F.  H.  (Negative  Quantities),  373 

Lamb,  Charles,  106,  431 

Lambert,  204,  205,  294,  393 

Lambert,  General,  455 

Laplace,  18,  151,  155,  167,170,  172,  198, 
243,  249,  250,  475 

Lardner,  Dionysius,  11,  420 

—  Nathaniel,  398 

Larriva.  Don  Juan  (Cyc.),  459 
Latin  Numerals  (666),  489 
Lauder,  William  (A.N.),  179 
Laurent,  Paul  (on  Atoms),  187 
Laurie,    James    (Moon    paradox),    251, 
252 

—  Sir  Peter,  277 
Lausbergius,  Philip  (Cyc.),  46 
Law,  William  (Mys.),  151,  460,  461 
Lee,  Dr.  R.,  44 

Lee,  Prof.  (Orientalist),  78 

Lee,  Weyman,  93,  94 

Legendre,  136,  393,  499 

Leggatt  (martyr),  40 

Legh,  Peter  (Ombrology),  293 

Leibnitz,  4,  6,  40,  279,  308,  470 

Leisure  Hour,  The,  312 

Leland,  136 

Leo  X.,  Pope,  220,  285,  499 

Lettres  sur  1'Atlantide  de  Platon,  99 

Leverrier.  31,  53,  211,  237,  238,  239,  241, 

242,  253,  343,  348,  451 
Lewis,  Sir  G.  C.,  358,  et  seq. 
Lexicon  Universale,  Hofman,  439 
Libri,  Guglielmo,  29,  41,  136,  448 
Library  of  Useful  Knowledge,  167 


INDEX. 


507 


LIL 

Lilly,  451 

Lipenius,  179 

Little,  James  (On  Logarithms'),  128 

Living  Authors  (Watkins  and    Shobcrl), 

431 
Locke,  John,  85,  86,  305,  326 

—  Richard  (Cyc.),  87 
Logan,  Rev.  Dr.  205 

Logical  Doggrel,  by  Sir  W.  Hamilton,  208 
London  Society,  The,  215 
Long,  St.  John,  2,  274,  386,  387 

—  George,  444,  445 

Longitude,  The,  discovered  (Winston),  87 

Longley,  Archbishop,  197 

Longomentanus  (Cyc.),  65 

Lotteries,  168 

Louis  XVIII.,  107 

Louis  Napoleon,  77,  289 

Lovett,  R.  99 

Lowe,  Robert,  (Decimal  Coinage),  363  to 

370 

Lowndes,  249 

Lubbock,  Sir  John,  167,  168,  174,  348 
Lucas,  Frederic,  267 
Lunar  Motion  (Jellinger  Symons),  304 
Lunn,  J.  R.  (Calculation),  292 
Luther,  Martin,  37,  HI,  285,  403 
Lycabettus,  Mount,  361 
Lyndhurst,  Lord  Chancellor,  118 


MACAULAY,  Lord,  83,  190,  191,  281, 
282,  455 

Machine,  Steam,  (Jonathan  Hulls,)  88 
Macclesfield  Letters,  448,  ct  stq. 

-  Earl  of,  6,  450,  4.')1 

Mac  Elshender,  John  (Moon    Paradox), 

305,  306 
Mackey,  Rev.  John,  214 

—  Sampson  Arnold,  151,  463 
Macchiavel,  144 

Maclear,  Sir  Thomas.  370 

Mac-leod,  H.  Dunning,  372 

Mac  Cook,  214 

Magliabeochj  Library,  418 

Magnus,  Baveme  and  Cocker,  30 

Magus,  Simon,  33 

Maitland.  Rev.  Samuel,  43,  97 

—  Hist,  of  London.  69 
Malacarne  (Cyc.),  71 
Manning,  Revd.  Henry  E.,  406 
Mansel,  Revd.  Dr.  ( Phrontisterion),  358 
Mansuete,  Father,  282 

Marcelis,  Jacob  (Cyc.),  77 
Margarita  Philosophic*,  The,  439 
Man-vat,  Captain  (Dog  Fiend),  306 

—  Samuel,  283 

Mai-tin,  R.,  M.P.  for  Gal  way,  409 

-  Old  Ben,  91 

Martyrologium  Romanum,  290 
Mary,  Queen,  223 

Maseres,  Francis.  117.  121,  122,  123 


MOB 

Mason,  Monk,  337 
Mathematical  Society,  New,  236 
—  Old,  230,  ft  seq. 
Mathers,  Patrick,  124 
Maty,  Dr.,  17,  18 

Maupertius  (Macclesfield  Letters),  451 
Maurice,  Revd.  F.  D.,  315 
Maurolycus,  72 

Maximilian,  Emperor  of  Germany,  439 
Maxwell,  Alexander,  63 
Mecanique  Analytique   (Lagrange),   189 

—  Celeste,  250 

Mechanic's  Magazine,  213,  344,  347,  350, 

351 

Medical  Reform  (Letter  on),  159 
Medici,  Cosmo  de',  448 
Melanchthon  (or  Schwartzerd),  464 
Mesolabum,  The  (Slusius),  71 
Mercator's  Planisphere,  309 
Mersenue,  Father,  65,  448,  449 
Meslier,  Jean,  379 
Messange,  Mallemont  de,  471 
Methode  Jacotot,  (P.  Y.  de  Sepres),  167 
Metius,  Adrian,  62 

—  Peter,  35,  62 

Metou  (Lunar  Calendar),  361 
Metonic  Cycle,  221 
Mill,  James,  154 

—  John  Stuart.  353,  408 
Milirr,  S.  (A.N.),  100 

—  Joe  (Story  from),  108 
Milne,  Mr.,  Actuary,  172 
Miluer,  Dr.  Isaac,  148,  149 

—  Lamp,  149 

—  Rev.  John,  263,  264,  265 
Milton,  John,  113,  465 
Milward,  RL,  418 
Minerva  Press  Novels,  114 
Modestus,  St.,  289 
Mollendorf,  Marshal,  250,  474 
Monthly  Magazine,  144 
Montmort  (Macclesfield  Letters),  451 
Montague,  Charles   (Lord   Halifax),  456, 

457 
Montucla,  30,  31,  32,  37,  43,  44,  57,  67, 

71,  72,  95,  96,  97,  179,  288,  470,  490 
Moon-hoax,  The,  337 
Moon  Controversy,  India,  262 
Moon  Paradox,  303,  304 
Moore,  Dr.,  113 
More,  Hannah,  113,  et  seq. 

—  Henry,  73 
Morgan,  Sylvanus,  5 

—  Lady,  114 

—  William,  133 
Morhof,  41 
Morin  Sieur,  62 
Morinus,  J.  B.,  89 

Morland  (Macclesfield  Letters),  450 
.Mormon.  The.  Newspaper,  291 
Morning  Post,  The,  173,  198 
Morrison,  Lieut.  (Zadkiel),  '-'77 


508 


INDEX. 


MOS 

Moses,  41 
Mouton,  102,  450 
M.  P.'s,  an,  Arithmetic,  417 
Muggleton,  Lodovick,  244 
Muggletonians,  The,  244,  245,  246 
Murhard  (Cyc.),  31,  44,  179 
Murphy,  Arthur    (Tr.  of  Tacitus),  454, 
455 

—  J.  L.,  285 

—  P.    (Weather  Almanac),     198,     199, 
246 

—  Kobert,  214 

Murray,  John  (Publisher),  111,  346 

—  Lindley,  466 

—  Mungo,  (Astronomical  lecturer),  456 
Museum  Collection,  The,  449,  tt  seq. 
Musgrave,  Abp.,  196,  197 

Mydorge,  179 

Mystery  of  Christ  (Behmen),  460 

Mystrom  (Tonal  System),  370,  371 


NAMES  of  the  Beast,  403,  et  seq. 
Napier's  Bones,  473 
Napier,  John,  45,  46,  53,  54,  70 
Napoleon    I.,   137,   145,   249,  250,    352, 

427 

Napoleon  III.,  77 
Nautical  Almanac,    180,    181,  182,  347, 

348,  369,  460,  485 
Nauticus,  (Cyc.),  333,  335,  353 
Neal,  Archbishop  of  York,  376 
Neal's  History  of  the  Puritans,  61 
Neptune  (Planet),  236,  et  seq.,  253,  343 
New  and  Full  Moon  (Table),  227 
New  Testament,  23,  386 
Newton,  Sir  Isaac,  4,  5,  6,  18,  21,  48,  49, 
50,  53,  54,  56,  66,  78,   81,  82,  83,  85, 
86,  87,   88,   91,   92,   96,   98,   100,  117, 
134,  135,  143,  152,  156,  187,  188,213, 
231,  235,  243,  244,  245,  250,  275,  294, 
305,  340,  345,  355,  432,  446,  449,  451, 
456,  463,  469,  472,  478,  479 
Nicene  Creed,  228 

—  Council,  220,  228 
Nicholas  of  Cusa,  33 
Nichols,  (Anecdotes)  104,  154 

—  Dr.  444 

Nicolas,  Sir  Harris,  217 

Nicollet,  197,  198 

Nieuwentiit,  470 

Notes  and  Queries,  9,  66,  90,  91,  98,  114, 

115,  116,  146,  151,  153,  245,  265,  266, 

268,  418 

Number  of  the  Beast,  401,  et  seq. 
Nursery  Rhymes,  349 


OCCAM,  275 
Odgers,  Nicholas,  376,  377 
Oldenburgh,  450,  455 
Oliver  Twist,  394 


POE 

Oughtred,  450,  451 ,  456 

Owenson,  Sydney,  (Lady  Morgan,)  114 

Ozanam,  189 


PAINE,  Thomas,  102,  104,  110,  143 
Paley's  Evidences,  402 
Paley,  William,  133,  146 
Palmer,  Charles,  134 

—  John  (Mail  coaches),  419,  420 

—  Thomas  Fysshe,  420 
Pallieur,  65 

Palmerston,  Viscount,  174,  216 

Panizzi,  Antonio,  90,  244 

Papist  and  Protestant,  265,  et  seq. 

Paracelsus,  403 

Pardies  (Macclesfield  Letters),  451 

Paradoxers  (Ways  of),  3  et  seq. 

Park,  Mungo,  309.  337 

Parsey,  Arthur  (Cyc.),  176,  177 

Parr,  Dr.  Samuel,' 103,  104,  105,  109 

Pasbergius,  Manderupius,  235 

Pascal,  Blaise,  30,  62,  132,  296,  475 

Passot  (A.N.),  167 

Passover,  Jewish,  226 

Patrick,  St.,  331 

Paucton,  103 

Paulian,  Father,  98 

Peacock,  Dr.  (Dean  of  Ely),  117,  214 

Peel,  Sir  Robert,  155,  215 

Peel,  Yates,  174 

Pell  (Macclesfield  Letters),  65,  450 

Pemberton,  81 

Penny   Cyclopaedia,   173,   214,   261,   266 

439,  et  seq.,  460 

Penny  Cyclopaedia  (Supplement,  60,  61) 
Pepys,  W.,  69 

Perigal,  Henry,  (Moon,)  261,  262 
Perpetual   Motion   (Predavul),  213,  285, 

286,  342 
Perspective,  176 

Peters,  William  (Cyc.),  255,  459 
Petit,  Andre,  186 
Petty,  Sir  William,  69,  450 
Philalethes,  Eugenius,  151 
Phillips,  Sir  Richard,  143,  144,  145,   152 
Philo  of  Gadara,  30 
Philosophia  Sacra,  140,  141 
Philosophical    Transactions,    214,     422, 

436 

Pike,  Samuel,  140 
Pilgrim's  Progress,  447 
Pindar,  434, 
—  Peter,  433 
Piozzi,  Mrs.,  433 
Pitt,  Earl  of  Chatham,  123 
Place,  Francis,  119,  120 
Platts,  Rev.  J.,  266 
Playfair,  Professor,  138 
Pliny,  215,  439  ' 
Ploucqiiet,  204.  205 
Poe,  Edgar,  337 


INDEX. 


500 


rot 

Poisson,  176,  250 

Pons  (Comet  Finder),  279 

Pope,  Alexander,  436 

Porta,  J.  Baptista,  45,  53 

Porteus,  Bishop,  115 

Poms  of  Nicaea,  30 

Powell,  Baden,  430 

Praed,  Winthrop  Mackworth,  371 

Pratt,  Dr.  H.,  354 

Pratt,  Orson  (Mormon),  294 

Predaval,  Count  de,  213 

Prescott,  Bartholomew,  161,  167 

Prester  John,  47 

Price,  Richard,  133 

Prince  Consort,  342,  343 

Princess  Alexandra,  243 

Protimaletb.es,  252 

Pseudochrist  and  Antichrist,  252 

Pseudomatli,  Philomath  and  Graphomath, 

473,  et  seq. 
Ptolemy,  425 
Pujos,  M.,  1 79 
Puseyism,  43 

Pyramids,  The,  308,  311,  377 
Pythagoras,  151,  287,  367 


QUARLES,  Philip,  436 
Quartadecimans,  The,  220 
Quarterly  Review,  346,  385 
—  Church  of  England,  192 
Q.  E.  D.,  255 
Quintilian,  439 
Quotem,  Caleb,  246 


T>ABELA1S,  64,  124 

It     —  (Imitation  of),  125,  et  seq. 

Racovian  Catechism,  85 

Raleigh,  Sir  Walter,  467 

Rambler,  113 

Ramchundra,  231 

Ramus,  Peter,  4 

Raymarus  (Nicolaus),  35 

Real  Character,  Wilkins',  70 

Reasoner,  The  (Holyoake),  274,  et  seq. 

Recalcati  (Cyc.),  389,  458 

Recherches  Curieuses  des  Mesures,  &c., 

46 

Recorde,  Robert,  467,  468 
Reddie,  James,  371,  372,  477,  478,  479, 

et  seq. 

Reform  Bill,  191 
Reisch,  Gregory,  439 
Religion  and  Philosophy,  273,  274 
Religio  Laici  (Dryden),  295 
Religious  Tract  Society,  85,  86,  87,  114, 

115,  116,  117,  141 
1  Remains'  The  (of  Bacon),  86,  87 
Renatus     Franciscus    Slusius    (Mesola- 

bum),  71 
Reuchlin  (or  Capnio),  464 


BAN 

Revilo  (Oliver  Byrne),  142,  199,  200 

Reyneau,  45 

Reynolds,  Sir  Joshua,  202 

Rheticus,  46 

Ribadeneira,  290 

Richards,    George    (Camb.   Prize    Poet), 

431,  432 

Richardson,  Samuel,  121 
Richelieu,  Cardinal  (Official  Report),  62 
Rigaud,  John,  450 

—  Stephen,  83,  450,  452 

Rights  of  Boys  and  Girls  (Parr),  103,  104 

—  Man  (Paine),  103,  104 

—  Woman  (Wollstonecraft),  103,  101 
Ringelberg,  439 
Ripley,  Sir  G.  (Ale.),  75 
Ritchie,  Rev.  W.  (Geometry),  177,  178 
Rittershusius,  40 
Ritualism,  43 

Robertson,  Dr.  (Hutcbinsonian),  140 
Roberval,  65 
Robinson,  Bryan  (on  Ether),  88 

-  Dr.  (Armagh),  370 

—  H.  Crabb,  283,  435 

—  Robert,  106 
Roblin,  Justin,  341 
Rock  of  Ages,  The,  141 
Rogers,  Samuel,  425 

Roget,  P.  M.  (Thesaurus),  246 

Rokeby,  or  Rookby,  470 

Roman  Christian,  263 

Romanus,  Adrianus,  67 

Ross,  Capt.,  182 

Rosse,  Earl  of,  20 

Rossi,  Gaetano  (Cyc.),  137 

Rough,  Serjt.,  118 

Ro.wning,  93 

Royal  Naval  Club,  166 

Royal  Observatory,  Berlin,  238 

Royal  Society,  The,  16,  17, 18,  19,  20,  21, 
22,  38,  39,  66,  69,  80,  97,  98,  122, 167, 
176,  238,  374,  375,  376,  422,  436,  455, 
456 

—  Committee  of,  449 

—  (Signatures),  422 

—  (Library),  83 

—  (Transactions),  20 
Rudolf,  Chr.,  499 
Russell  (Printer),  110 
Russia  (Meteorology  in),  54 
Rutherford,  W.  (Cyc.),  374 


SABBATARIANISM,  311 

O     Sabelliatism,  142 

Sabben,  James  (Tris.),  255 

Sacrobosco,  221 

Sadler,  Dr.,  141,  142,  143 

Sadleir,  Dr.  Francis,  155 

Salmasius,  362 

Salicettus,  Th.  (Gephyrauder),  43,  44 

Sam  Slick,  337 


510 


INDEX. 


SAN 

Sanchez,  Peter,  136 

Sanders,  M.  A.,  124 

Saturday's  Moon,  A,  195 

Saunderson,  80.  232,  451 

Scaliger,  Joseph,  31,  67,  68,  353,  410 

—  Julius,  68 
Sara,  Kobert,  179 
Schopp,  41 

Schoolboy's  Defence,  A,  411 

Schott,  Caspar  (Ale.),  43,  44,  291 

Schwal,  137 

Scott,  Walter,  15,  20,  34,   35,  78,   114, 

427,  469,  474 

Schumacher,  Prof.,  65,  66,  449 
Scriptural  Calendar,  256 
Scripture  and  Science,  426,  427,  428 
Selden's  Table  Talk,  418 
Senarmont,  M.,  280 
Sentinel,  The,  297 
Shaftesbury,  Earl  of,  370 
Shakspeare,  10 

Shanks,  William  (Cyc.),  290,  291 
Sharpe,  Granville,  141 
Shaw,  Peter,  84 
Sheepshanks,  John,  88 

—  Richard,  174,  175,  344 
Shepherd,  Attorney  General,  74,  107 
Sheridan,  Tom,  104,  105 
Simpson,  Thos.,  232,  451 

Simson,  Eobt.  (of  Kirktonhill),  117,  120, 

121,  138 

Sinclair,  Prof.,  124 
SKii/Sainros,  268 
Sloane,  Hans,  18 
Slipslop,  Misses,  466 
Slusius,  450 
Smith,  Ambrose,  170 

—  James  (Rejected  Addresses),  336 

—  Rev.  James,  287,  288,  378 

—  James    (Cyc.),    32,    316,    et    seq.    to 
337    (inc.),    352,   353,   354,  356,  357, 
389,  390,  391,  408  to  416  (inc.),  460, 
472  to  477  (inc.),  488,  489 

—  Sydney,  163 

—  Thos.,  211 
Smithfield  Burnings,  40 
Smollett,  113 

Smyth,  Piazzi,  292 

Siiell,  Willebrord,  48 

Socinians,  The,  85.  447 

Socinus,  Faustus,  3,  85 

Socrates,  220 

Sohnke's  BibHotheca  Mathematica,  337 

Solar  Parliament,   The,    181,    182,    183, 

184 

Somerville,  Mary,  143 
Somnium  Ciceronis,  &c.  (Home),  90 
Southcott,  Joanna.  287,  313 
South,  Sir  Js.  370 
Spearman,  140 
Spedding,  James,  49,  53,  85 


THI 

Speed,  John,  120 

Speke,  Captain,  46 

Spencer,  Earl  (The  late),  254 

Spinoza,  Benedict,  3,  29 

Spiritualism,  286,  287,  288,  378,  et  seq. 

Spurius  Cassius  and  Spurius  Melius,  476 

Stapulensis,  Faber,  31 

Starkie,  George,  75 

Statter,  Dover,  301 

Steel,  James,  293 

Stephens,  Henry,  31 

Stevin  and  Dumortier,  189 

Stephenson,  George,  342 

—  Robert,  342 

Stevinus,  Simon,  53,  189,  190,  288 

S'-.ifelius,  Michael,  499 

Stiles,  John  (Camb.  Carrier),  453 

St.  Martin,  Louis  Claude,  100,  101 

St.  Mesmin  (Menut  de),  168 

Strafford,  Lord,  142 

Stratford,  W.  S.,  180 

Stukeley,  Dr.,  140 

St.  Vincent,  Gregory  (Cyc.),  67,  70 

Substitute  for  Declaration  of  Belief,  424, 

425 

Suffield,  George,  292 
Sullamar,  Henry  (Cyc.),  179 
Sumner,  Bishop  of  Chester,  196 

—  Bishop  of  Winchester,  196 
Sussanoeus,  Hubertus,  35 
Suvaroff(at  Ismail),  305 
Swedenborg,  Emanuel,  151 
Swedenborgians,  The,  287 
Swift,  Dean,  79,  80 
Sylvester,  Professor,  472 
Symington,  (Engineer,)  88 
Symons,  Jellinger,  251,  261,  304 
Sympathetic  Powder,  16,  66 


rriABLEAU   Naturel  des  Rapports,  &c. 

1     (St.  Martin),  102 

Tablet,  The,  266,  267 

Talbot,  Sir  Gilbert,  16,  66 

Tarporley,  451 

Tartaglia,  288 

Tassius,  65 

Tate,  Rev.  James,  119 

Tauler,  John  (Mys.),  463 

Taylor,  Brook,  451 

—  John  (on  666),  216 

—  John,  311,  312 

—  Robert,  (Devil's  Chaplain,)  161,  162, 
166 

—  Thomas  (Platonist),  112 
Teissier,  Anthony,  68 
Tenterden,  Lord  Chief  Justice,  108 
Tetragonismus,  31 

Thales,  288,  303 
Thelwall,  John,  106 
Theophrastus,  361 
Thiebault,  250,  474 


INDEX. 


511 


THO 

Thompson  (Gen.  Perronet),  173,210,  3^2, 

373 
Thomson,  Archbishop,  197 

—  Dr.  (Hist.  Royal  Soc.),  16 
Thorn,  Rev.  David,  402,  et  seq. 

—  J.  Hamilton,  402 
Thorndike,  Dr.,  457,  458 

Thorn,  Dr.  (666,  &c.),  355,  356,  357,  358, 

394  to  408,  489 
Thrale,  Mrs.,  1 43,  433 
Thurlow,  Lord,  133 
Thyracus,  35 
Tippoo,  35 

Torriano,  Evangelists,  148 
Towneley.  451 
Tractarianism,  42,  43 
Transmigration,  310 
Trinity,  The,  (Illustrated  by  Astronomy,) 

103 

Trinitarianism  of  Bacon,  86 
Trochoidal  Curves,  261 
Troughton  and  Simms,  90 
Turner,  Mr.  (Newton's  apple-tree),  81 
Tycho  Brahe,  49,  235,  451,  471 

TTNITARIAN  Controversy,  402 
U      Unitarians,  The,  266,  268,  447 
United  Service  Journal,  258 

—  Magazine,  253 
University  College,  153,  268 
University  of  London,  153,  156 
Upton,  W.  (Tris.),  256,  257,  258 
Urban,  Pope,  430 

Useful  Knowledge  Society,  192,  442,  444, 

447 
Useful  Knowledge,  Library  of,  167 

T7ALENTINE,  Basil,  (Ale.),  74,  75 
V      Van  Schooten,  288 
Verses  on  Paradoxers,  484 
Verses  on  the  Roundness  of  the  Earth,  309 
Vestiges  of  Creation,  210,  211 
Viceroy  of  Egypt,  290 
Victorinus  of  Aquitaine,  221 
Victoria  Toto  Coelo,  (J.  Reddie,  372) 
Vieta,  67,  390,  448 
Village  Dialogues,  114 
Vitruvius,  439 

Vitus,  St.,  289,  290,  438,  460 
Vivian,  103 
Voltaire,  64,  90,  146 

—  Chretien,  145,  et  seq. 
Vogel,  A.P.,  230 

Von  Gumpach,  341 

WALKER,  W.  E.,  459 
Wallis,  66,  450,  458 
Wallich,  Dr.,  257 
Walpole,  Horace,  17.  78 
Walsh,  John,  154,  155,  156,  157,  354 
Walter.  Peter,  Usurer,  435 
Warburton,  Henry,  37,  213 


ZYT 

Ward,  Seth,  450 

Wariug,  133 

Warner,  451,  457,  458 

Warren,  Samuel,  475 

Watt,  98,  104,  249 

Weddle,  Thomas,  373,  374 

Weld  (Hist.  Royal  Soc.),  16 

Wellington,  Duke  of,  190 

Wesleyanism,  43 

Westminster  Review,  173 

Whately,  Archbishop,  145,  146,  196 

Whewell,  Rev.  Dr.,  63,  317,  415,  416,417, 

430 
Whiston,  John,  87 

—  William,  79,  87,  93 
White,  Blanco,  146 

—  Kirk,  432 

—  Richard  (Albius,  Cyc.),  9 

—  R.,  66 

White  Stone,  The,  316 

Whitworth,  Professor,  477 

Whizgig,  The,  151 

Wightman,  G.,  40 

Wilkins,  Bishop  (Real  character),  62,  70, 

135,  338,  373 
William  III.,  310 
William  IV.,  176 
W7illiams,Thomas(Weights  and  Measures), 

102 

—  Mr.  (Sec.  Ast.  Soc.),  233 

-  R.,  Boston,  281 
Wilson's  Euclid,  477 

—  John  (Theorem),  132,  133 

—  R.  (Moon's  Rotation).  253 
Wingate's  Arithmetic,  455 
Wirgman,  Thomas,  153,  154 
Wiseman,  Cardinal,  266,  267,  447 
Wolzogen,  Baron,  65 
Wollstonecraft,  Mary,  103,  104 
Wood,  Anthony,  70 

Wood's  Athenae  Oxonienses,  461 
Wood,  Jean,  138 
-William,  145 

Woodley,  Captain,  R.N.,  185,  186 
Wordsworth,  William,  435 
Wright,  Thomas,  90,  91 
Wronski,  Hoene,  148 
Wrottesley,  Lord,  379 

TOUNG,  Brigham,  294 
-  Dr.  Thomas,  18,  22,  148 
Yvon,  Paul,  178 

F7ACH,  Baron  (Solar  Spots),  279,  380 
LJ     Zachary,  Pope,  24,  ct  seq. 
Zadkiel's  Almanac,  195,  277,  472 
Zetetic  Astronomy,  306,  307,  308 
Zodiac  of  Denderah,  34 1 

-  Esnd,  341 

—  Palmyra,  167 
Zypceus,  101 

Zytphen  (A.C.),  471,  472 


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